Hi Giles Wembley-Hogg,
I insist it is extremely unlikely to get a CLIMB RA while descending like a rocket.
Don't get me wrong, I'm not saying it is extremely unlikely to get an RA while doing so, on the contrary, I believe the chances for it increase.
But you definitely won't get a CLIMB RA.
One of the basic principles of TCAS is that it is designed to suggest the smallest correction necessary to the actual flight path.
Can you believe an airplane descending like a rocket getting a CLIMB RA?
Nope!
The rate is so high, that you will get a MONITOR VERTICAL SPEED RA, to reduce it, or maybe even maintain it, as the TCAS will take advantage of this high rate and make the other traffic climb.
But certainly you won't get a CLIMB RA.
A bit of speculation, I know, but if you know the system and some previous incidents, you will come to this conclusion.
Having said that, I'd like to add that in the beginning it was encouraged to selecy TA ONLY in single engine and similar circumstances.
Not anymore.
Now the trend is to ALWAYS leave TA RA selected, as TCAS is perfectly capable of calculating the right maneuvres to be accomplished, even if one of the two airplanes (the one in the emergency descent) does not follow it.
The other one will get a revised RA, but as long as you don't make the worst possible mistake of maneuvering CONTRARY to the RA, everything will be fine.
Remember, if in doubt about the RA, at worst don't do anything..
Still OK if the other one has got a TCAS.