One would think air in the fresh water intake should go away pretty quickly.
I've a length of clear hose I hook to our normal intake for pumping anti-freeze through the system prior to winter lay-up. Naturally, when I first hook that in, it's got nothing but air in it. Soon after starting the engine the entire length, about three feet, is solid purple all the way. I can't even tell the water is moving by looking at the hose.
In the case of a strainer, I guess it would depend on where the intake and output are. If the intake is on top, where the bubble is, I guess I can see it remaining. Unlike Steve, tho, I can't see it much affecting water flow rate.