The antenna that is not in the right polarization will be about 3dB down.
Since it get a weaker signal, it will be selected less often.
In a case where you have PC antennas (tend to be vertical polarization) and laptop NICs with built in antennas (like the Cisco, which tends to be horizontal polarization), perhaps some benefit could be gained, I can't say I've ever measured or monitored it in that config.
Good Luck
Scott