Sounds like an awful idea in general. Think KISS concept. But you'd have to look at manuals. There's probably no single answer. (I was thinking of wireless control of the thermostat itself.)

I'd add that, where I live (New England), furnace failures can be basically catastrophic so any theoretical convenience advantages just aren't worth it.

That depends. Sometimes because they have encryption. It isn't hard to have shared keys of some sort. If there is no internet connection on the link (which is possible - I've never seen where both systems connect to wifi, but if they do worry!), and so you don't have to worry about malicious hackers and in turn the encryption is good enough even if done somewhat wrong.

Sometimes they are just send a radio signal and hope nobody else in range is using that frequency.

So again, there are too many different ways this is done to guess. Unfortunately they probably don't put this in the manual.