Let's say two Wi-Fi access points (AP1 and AP2) are set up very close to each other and on the same or adjacent channels. If AP2 is idle (has no clients associated or none that are transmitting or receiving data), does it interfere with AP1 to a practically significant extent? I'm aware AP2 would be transmitting beacon frames usually every 100 ms, but I imagine that the amount of interference this alone causes would be negligible.
Your hunch is correct, idle APs on the same channel don't create enough interference to be a problem. Doing a little back-of-the-envelope calculation, I think beacons from a single idle AP would typically take up only about 2% of the available airtime on a channel, and that's for almost a worst-case of a 2.4GHz AP that still has the ancient 1 mbps data rate enabled, and is using that for beacons. A 5GHz AP — or a 2.4GHz AP set to use only G rates or better — would use just one-sixth of that or less, because its minimum basic rate would be at least 6 mbps.
You'd probably see a bigger hit if one of the APs — or other in-range devices, even if idle — was B-only, because it would cause G and N gear to have to jump through some extra hoops to use more modern data rates without stomping on (or getting stomped by) the B device. These protection mechanisms may have more than a 2% hit.
If you have control over the APs, it's better to be on the same channel than a partially-overlapping channel, because the protocol is designed to detect and handle the same-channel case well. Of course completely separate non-overlapping channels is best.