FNG here. Private Pilot and aircraft owner-PA-28. It is good to see that there are some real experienced folks here, adding good info and not just crazy conspiracy theories.
As for transponders, every aircraft registered, at least in the USA, has a unique transponder address assigned, whether a xpdr is installed or not. For instance, my PA28 has a Mode C transponder, which as far as I know does not broadcast any identifying info other than whatever code I have dialed into it.
AFAIK the address code is reserved for future use. Of course in the airline and commercial world where more sophisticated xpdrs are required (and soon for GA too, with the impending ADS-B requirements), the address is coded in and transmitted on the extended squitter.
As far as simming goes, at least in the GA world I hear it is getting quite popular as a tool to maintain skills when one can't fly as often as one would like. My CFII has said he uses FSX as a tool to brush up on instrument procedures, and recommends it to his students. I personally fly XPlane 10 a lot to keep up when the weather keeps me grounded (still working on my inst rating and of course a PA-28 is not certified for flight into known icing). Simming is a tool that I would bet a lot of commercial and ATP pilots use for fun and informal training, nothing inherently suspicious there.