Ron, W4TQT wrote:
"Question: would an antenna having gain capture any more signal than a
completely omnidirectional antenna with no gain?"

Directive gain depends entirely on the distribution of radiated power.
See 1955 Terman page 870. The antenna gain figure is identical for
transmitting or receiving. To take full advantage of gain in a line of
sight path, the electric vector must be parallel with that received.
Cross polarization can cause up to almost 30 dB signal loss. There are
directional antennas that receive vertical and horizontal polarizations
equally well.

Yes. An antenna with gain captures more signal than an antenna with no
gain when both are in their best positions and equally distant fron the
same signal source.

Best regards, Richard Harrison, KB5WZI