In Europe, it is only military transport type aircraft (MTTA) that are being required to carry TCAS - either under a voluntary programme or by legislation (Germany).
Is Nimrod a MTTA? - I would suggest not as it is regarded as a reconnaissance aircraft for Diplomatic Clearance purposes. So it would not need any "waivers" - unless someone is being very liberal with their interpretation of what defines a MTTA.
I don't think that the FAA have got so deeply involved as the ECAC regulatory authorities, probably because the US military has the muscle to refuse to accept any mandates that it doesn't like. The USAF decided to fit TCAS to all it's transport-type aircraft following a mid-air between a C-141 and a Luftwaffe Tu-154 off West Africa; a lesson that the UK MoD ignored until the German legislation forced their hand. I don't know whether this USAF programme extended as far as multi-engine non-transport types such as B-52, B-1B etc, but if they did I suspect that this will have been at their own volition and not as a result of FAA regulation. I'm fairly sure that as a military aircraft Nimrod can operate in US airspace in the same way that RAF fast-jets frequently do.