Do interceptor squawk codes suppress TCAS RAs?
To avoid an RA, the interceptor would almost certainly turn off at least his Mode C, and to avoid a TA and the concern in the intercepted aircraft of "what is this no-altitude traffic doing closing rapidly on me???" he will probably turn off his squawk altogether before he gets to the last few miles of the intercept.  (There were cases years ago when TCAS was pretty new of intercepted aircraft getting a series of RA's as interceptors -- squawking everything -- closed on them, maneuvering to continue the intercept even as the target climbed and dived all over the sky in response to the RA's. That scenario is undesirable for all sorts of reasons!)

A wingman may well hold a squawk and park himself some miles in trail of the target, monitoring both the interceptor and the target with his own air-to-air radar.  ATC can see the wingman and the target, and knows that there is an interceptor somewhere between them -- which is probably enough for their purposes.

Each specific case probably has letters of agreement between the ATC facility and the specific interceptors, so they'll all know in advance who's where, doing what, squawking or not squawking what, and who's talking on which frequencies.  Those sorts of specifics probably aren't available in the public domain.