Indeed, the transponder will be interrogated by several radar heads at any one time in most terminal areas for code - All the ACC ones plut the APP radars from every airfield in range.
However, without getting into sort boxes etc, for an ACC sector, the information received from several heads will be compared and the best response displayed to the controller i.e. the response from a single head. Thus in general, the controller will see an update every 6 seconds or so (screen refresh rate etc may delay this slightly).
For an airfield, in general a single head is used but as I said these rotate faster.
For the airfields and ACC sectors not interested in your flight, it will be ignored or perhaps even filtered out.
As for TCAS - does TCAS use the code select element or simply the source of a signal and Mode C?
Regards,
DFC