I don't think they do. I used to set it off the nearest AWOS/ATIS if out in the sticks. Non-radio I'd imagine you could either set airfield elevation before you took off, or found the info from 1-800-WX-BRIEF or one of the other decent weather briefing services you can get out in the US prior to departure.
I wouldn't be so certain everyone in a specific UK ASR is on the same setting... The number of initial calls you hear from people requesting a radar service, and on being asked to pass details your hear all sorts of varying QNH/QFEs reported. Then you might get people transiting a zone, with the airfield QNH set, while they're on a basic/traffic service OCAS (where everyone else is on the RPS), or some even at a flight-level. Then there's the ones not talking, doing whatever they want OCAS.
Never heard this 29.92 all over the place thing though, that's news to me.