Without double checking, I believe our SOP is to notify ATC when we are to submit an ASR for a TCAS RA. I think calling it flags the fact up to (particularly in this case) a busy ATCer and confirms the fact that we had an incident.
When we declare "TCAS RA" on the radio, an acknowledge is really useful because we know that ATC are now aware we are deviating from our clearance and hopefully will be moving airplanes out of our way. A response of "Roger, report clear" is useful, I thought it was now standard?
It is quite disconcerting when you get an RA and cannot hear the other aircraft but I have had one where the aircraft was on another frequency. We had to make further inquiries to find out basic info for the other aircraft to help with the report.