One problem with foregoing ventilation during cardiopulmonary support (CPS) is that severe hypoxia has profound hemodynamic and hemo-rheological consequences. It is difficult to restore adequate mean arterial pressure (MAP) in the presence of hypoxia and acidosis (especially under the impoverished flow conditions of closed chest CPS). This problem is compounded by hypoxia and acidosis-induced changes in red cell fluidity (red cells become rigid when depleted of ATP), hypoxia-induced alterations in red cell aggregability, increased platelet and white blood cell adhesion, and alterations in the character of the glycocalyx (increased stickiness) which lines the capillaries all further compromise perfusion. In fact, these changes greatly impede restoration of any microscopic tissue perfusion. Similarly, within minutes of cardiac arrest, there is nearly universal edema of both the capillary endothelial cells and the tissue parenchyma due to collapse of ion regulation; the sodium/potassium pumps run out of energy and cease to operate. This phenomenon is particularly pronounced in the brain and is likely a major contributor to the no-reflow phenomenon (failed reperfusion of the microcirculation). Re-oxygenation and the restoration of metabolism and effective cellular ionic pumping is thus very attractive because (at least historically) it is the only approach that offers the prospect of restoring effective perfusion which is necessary both in order to cool rapidly and to distribute cerebroprotective medications (especially absent extracorporeal support).
Of course, this is mostly just theory based on gedanken experiments and very limited laboratory investigations. It is certainly true that some cryopatients unequivocally benefit from aggressive reperfusion with ventilation as evidenced by return of good tissue perfusion and even the return of neocortical electrical activity (and if un-medicated, return of consciousness). However, most cryopatients are far too seriously injured by peri- and post-arrest disease and hypoxia-ischemia to respond in this way. What is really needed is systematic research in truly relevant animal models (i.e., following cardiac arrest from sepsis, hypovolemia in the setting of systemic inflammation, prolonged hypoxia, and so on) to determine if anoxic (closed chest) CPS can be made workable or even superior to CPS with ventilation. Administration of a hypertonic solution to reverse flow-inhibiting edema and containing drugs which reverse blood cell and glycocalyx stickiness and raise perfusion pressure to acceptable levels (without the need for ventilation) is a very attractive idea since it offers the prospect of side-stepping oxygen radical mediated reperfusion injury.
In the past, the only pressors in the resuscitation armamentarium were alpha adrenergic agonist drugs typified by epinephrine. None of these drugs are useable in the presence of acidosis because the alpha adrenergic receptors do not function in acidosis. With the advent of the use of vasopressin and related V1 receptor agonists in resuscitation and critical care medicine it is now possible to raise MAP in the presence of acidosis. Recent research has also made it abundantly clear that epinephrine (and at least some other alpha adrenergic agonists) impair cerebral blood flow during CPR, compromise the microcirculation, and undesirably increase cerebral metabolism (for these reasons epinephrine should no longer be used as a pressor in cryopatient CPS). What is not known is whether vasopressin and anoxic CPS will provide adequate perfusion and superior cytoprotection as opposed to CPS with ventilation. The only way to answer this question is to do the necessary experiments.
Finally, even if the answer to this and related questions is discovered, the current dismal level of cryopatient “care” would make application problematic; anoxic CPS presents its own formidable technical challenges and is conceivably more difficult to implement properly than is conventional CPS with ventilation. There have recently been many powerful advances in critical care and resuscitation medicine (both research and clinical) which cry out for application in cryonics. However, this is not possible (and should arguably not even be attempted) until competence is first achieved in the application of the most basic (and long understood) elements of patient care. 
Compression-only CPR (with no accompanying positive pressure ventilation) is still effective at generating some ventilation. This may seem impossible because the tidal volumes during compression-only ventilation are very small (~40 ml), in fact much smaller than the anatomical dead space of the large airways (~250 ml). In theory, all that should happen is that gas will move to and fro in the oropharynx and trachea with no ventilation of the alveoli and thus no gas exchange. In practice, modest gas exchange does occur due to pressure waves and stirring of the large airway gas presumably in a way similar to that in which gas exchange occurs in high frequency ventilation where tidal volumes are also very small (and well below the anatomical dead space). Deakin, et al., have measured ventilation in compression-only CPR in hospital patients who have failed resuscitation (Deakin C, O’Neill J, Tabor T. Does compression-only cardiopulmonary resuscitation generate adequate passive ventilation during cardiac arrest? Resuscitation , 75: 53 – 59C; 2003.) and found that median tidal volume per compression was 41.5ml (range 33.0–62.1ml), with a peak end-tidal CO2 of 0.93kPa (range 0.0–4.6kPa)and a minute CO2 of 19.5ml (range 15.9–33.8; normal range 150–180ml). While this not enough to support life it is more than enough to drive oxygen radical mediated reperfusion injury.
If compression-only active compression-decompression CPR (ACD-CPR) is used, minute ventilation rates (at ~100 compressions per minute) will be in the range of 2,500 to 3,000 ml with an alveolar ventilation rate in the range 1,200 to 1,500 ml/min. This is roughly a normal alveolar ventilation rate. In fact, gas exchange is somewhat better than would be predicted by the alveolar ventilation rate because non-tidal mechanisms of gas exchange (again, similar to those seen in high frequency jet and high frequency oscillating ventilation) come into play as a result of the high ventilation rate (100 breaths per minute) and the shock waves generated in the large airways as a result of chest compression. This effect becomes even more pronounced if high impulse CPR is being used in conjunction with ACD-CPR.
An added problem is that when cardiac arrest occurs both the arterial and venous blood will still have a large amount of oxygen present. Typically, life is not sustainable and death occurs when the central venous oxygen saturation (SVO2) reaches ~50%. Arterial blood oxygen saturation may range from just over 50% to as high as 98% depending upon the agonal course. While oxygen in the capillaries and small caliber arterioles and venules is quickly used up during circulatory arrest (ischemia) the oxygen in the large vessels persists for a long time after cardiac arrest. If circulation is restarted after a significant ischemic interval (>5 min) this reservoir of oxygenated blood provides a very damaging source of oxygen free radicals which cause reperfusion injury – even absent any exogenous ventilation.
The take-home message from the foregoing is that anoxic ventilation (ideally) would require more than simple occlusion of the airway; perhaps short-term ventilation with an inert gas (such as nitrogen) to facilitate desaturation of both the pulmonary blood (presumably nearly 100% saturated) and of the venous blood (~50% saturated). Inert gas ventilation may also be necessary to remove CO2. It will also be necessary to ameliorate red cell stickiness and rigidity as well as white blood cell and platelet adhesion and this will require pharmacological intervention; possibly inhaled nitric oxide, or more likely, intravenous administration of one or more nitrite compounds. It may also be necessary to provide some kind of substrate to provide energy to the vascular smooth muscle so that vascular tone and auto-regulation, and thus perfusion pressure, can be maintained during prolonged CPS. This will require formidable technical skill and thorough theoretical understanding. This is impossible given the current lack of biomedical acumen in cryonics.