squawkoff

I'm a controller at ZFW. We have been told that an aircraft in RVSM airspace is still RVSM capable if it looses its transponder. The equipment qualifier is an ATC assigned /H . I was under the impression that one of the requirements of operating in RVSM airspace, among many, is TCAS that is approved for RVSM. An aircraft that doesn't have a transponder or Mode C for that matter is invisible to other TCAS equipped aircraft. My question is will the TCAS system still talk to one another even with the transponder inop? Does TCAS get the information on the host aircraft from the transponder or from the Air Data Computer? I argued that the aircraft was no longer RVSM capable without a functioning transponder and mode? Management told me I was wrong.