If I fail to turn it on, ATC does not tell me to "pfchat217=Check your transponder. Squawk" (followed by the transponder code). If PF3 does not do that at some point, this would be a bug.
It is a bug....
Ah, ok. I'll try to give a precise short answer:
Transponder turned on can't be checked by PF3, because FSX does not provide this information. Therefore this is not a bug in PF3, but a missing feature of FSX.
Additional answer, unrelated to you original question:
Transponder code being correct can be checked by PF3, because FSX does provide this information. If this does not work, it would be a bug in PF3.
(and in all these answers you can substitute FSX with FS9 or P3D)