Ron wrote:
Assume an incoming rf signal has exactly the same strength in all 3
dimensions i.e., completely omnidirectional. Question: would an antenna
having gain capture any more signal power than a completely
omnidirectional antenna with no gain?

Ron, W4TQT

Yes.

The amount of signal "captured" from a given direction is exactly
proportional to the gain in that direction. "Capture area", "effective
aperture" and "gain" are simply different ways of expressing the same
thing, as long as perfect efficiency is assumed; if you know any one you
know the other two.

Roy Lewallen, W7EL