The issue of TCAS is an ongoing one - notably, the Tucano fleet at Linton On Ouse is presently being retrofitted with TCAS as a trial to gauge it's utility. The Vale of York is especially busy so offers an opportunity to evaluate it's use in a fairly high traffic density environment.
Having flown in both pre-mod and post-mod Tuc's, in my opinion the TCAS is a nice-to-have but not an essential. I found that in most cases, the traffic information it gave me occured after I had visually spotted the aircraft in question (we used it set to give an audible warning within a reasonably short range). So, as a lifesaver it could be useful but it didn't - and shouldn't - replace an effective lookout scan. Furthermore, in a high traffic density area, it was a distraction.
There is an argument for fitting TCAS to military aircraft, and as Mode S becomes more commonplace, the system should help to spot gliders, microlights etc which would previously have not been squawking. However, there are other issues, some of which you have touched on, such as weight and space. Also, there are certification issues, integration issues, emcon issues etc. Not to mention the cost! Weigh these against the utility, and the fact that the aircraft are designed to be used in war and not optimised for the UK, leads me to suggest that the advantage gained from TCAS may not be as great as you may imagine.
The original question related to the probability of a low flying military aircraft detecting a gyrocopter by electronic means. In my opinion (and I stand to be corrected) this is unlikely. A ground mapping radar is not optimised for detection of airbourne targets, and unlikely to be used for that purpose. TFR - forget it! There is no TCAS system in FJ aircraft yet. Do gyrocopters squawk? It is possible that the IR signature may be picked up on the FLIR, but I could not say how likely this would be.
However, as many of my more learned corespodents have suggested, the see and avoid principle works well when used correctly, and every effort is taken to avoid hitting a gyrocopter, hang glider or any other air user. I would suggest that, whilst every effort should be made to reduce them, collisions between air users should be viewed as a tragic but natural risk of the flying we all do in the restriced airspace available to us.
Blunty