I would worry that air in a HOB
filter might work its way into the intake tube, interfering with flow into the filter. Also, air in the media compartments could cause bubbles large enough to create dead/dry spots? However, wet/dry filters are the most efficient nitrification filters. But they are usually not designed to have air bubble up through them. Rather, the water usually trickles down over the media, or the media rotates through the water (biowheel).
I think more like BrianNY, bubbles or other surface agitation will likely make your tank fully saturated with oxygen for its temperature and salinity, and if you have enough oxygen for your fish to thrive you have way more than you need for your biologic filter.