Use of TCAS would be dictated by theatre IFF policy. It may well be possible that all transponder modes are employed - in which case TCAS would most definitely be switched on.
As stated Mode S and TCAS are not the same thing. Mode S in isolation does not really improve the safety of an individual aircraft, but does enhance the efficiency, and hence safety, of a suitably equipped ATC environment. The very few flight hours undertaken by non-equipped State aircraft does not degrade the concept.
TCAS requires Mode S to be fitted and then provides a huge extra safety margin for individual aircraft by providing collision protection from any other transponding aircraft - not just those also equipped with TCAS. Not surprisingly, the fitting of TCAS to it's passenger jets was forced on MoD by legislation in foreign countries and wasn't at their own volition. The bonus is that the system bestows tremendous safety and situational awareness benefits in all circumstances, particularly in operational environments that may have less well-developed ATC or even be operating on a procedural/VFR principles. It is short-sighted of the MoD not to fit TCAS wherever possible, and by not doing so they are taking the chance of mid-air collision "on risk".
RVSM for aircraft like the Nimrod is a different issue. It requires an updated altimetry system, an altitude alerter and an autopilot level lock. The fitting and clearance is not always straightforward on legacy aircraft and has to be weighed against the cost of limiting the aircraft to FL280. In theory, State aircraft are allowed into RVSM airspace , but ATC then have to provide 2000' separation and in practice the controller will simply refuse the request due to impact on other traffic. Similarly, aircraft like C-130 and Nimrod are incompatible with the civil traffic due to speed differentials, so would often not be given those levels even if they were RVSM compliant. Incidentally, this is a practical reality that appears not to figure in the claims for C-130J and A400M range/payload.
It is probably not worth giving Nimrod standalone Mode S or RVSM - but omitting TCAS is a wholly different risk.