This is an interesting idea, I believe that initially it was thought that bubble CPAP might deliver some high frequency pressure oscillations to the lungs, as the bubbling in the circuit causes some small amplitude variations in the pressure in the circuit. I think that has probably been debunked, there is likely no significant CO2 removal as a result of these small oscillations in pressure.
On the other hand if you hitch up your CPAP prongs to a real high frequency ventilator then you might be able to deliver some non-invasive high-frequency ventilation, at least while the airways are open.
This group of researchers (Mukerji A, Singh B, Helou SE, Fusch C, Dunn M, Belik J, et al. Use of Noninvasive High-Frequency Ventilation in the Neonatal Intensive Care Unit: A Retrospective Review. American journal of perinatology. 2014) report a retrospective group of babies who were treated with this kind of intervention. During high frequency non-invasive ventilation there was a reduction in apneas, in oxygen requirements and in CO2. Of course the question is what would happen to a similar group of babies treated with standard non-invasive techniques.
The only way to know is by doing an RCT, which I hope is being done.
Neonatal Research 
Hi Keith,
Kurt Albertine from Salt Lake City has been working on the sheep model of prematurity and lung injury for many years. As sheep have a rather long nose (snout?) and do not ventilate effectively with “regular” CPAP, they have been using high-frequency CPAP for many years and shown its benefit compared to IMV. E.g. http://www.ncbi.nlm.nih.gov/pubmed/24378898; http://www.ncbi.nlm.nih.gov/pubmed/18556628 etc
There are older human studies as well (but no RCT): http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1720809/
Would be useful to test by RCT, but the sample size needed would be 800-1200 to show incremental benefit. With declining NIH funding and trials more expensive, it is getting harder to do large RCTs these days.