To pursue the matter of TCAS useability with an engine failure, here's what Gulfstream told us on my (recent) G5 initial:
TCAS is fed with "standard" performance specs for the airplane you are flying, ALWAYS assuming all-engine. When in conflict with another airplane, both TCAS also "exchange" their aircraft type. Due to the very high performance of the G5, and if a resolution advisory occurs, the G5 will get the "CLIMB CLIMB" end of the deal.
Accordingly, one item on the "Engine failure in flight" checklists is the switching of the TCAS to "TA only". This will not only prevent our own aircraft from displaying RA's outside of the envelope, but it seems (instructor said so...) that the box will actually transmit the fact that we are in "TA only" mode. What I don't know is how that transmission could or should affect the other party in the conflict...
Anybody know more about the intricacies of TCAS in these situations?