RF measurement setup
The setup looks fine, IMO, however, I highly doubt you'll see ambient WiFi signals coming through without some sort of amplification, especially if the noise floor of your spectrum analyzer is not that great. You may have some luck if you put your WiFi source much closer to the antenna (and oriented correctly, which will depend on the far-field radiation patterns of the antennas), but even that may be problematic.

As mentioned in comments, BNC isn't an ideal connector for this, but I don't think it should be a real issue. Microwaves101 lists BNC as rated up to 4GHz.

I don't have any realistic numbers off the top of my head, but I'd guess you'd need a noise floor lower than say -80 or -90 dBm to distinguish any ambient WiFi signals from noise.