Usually (E)GPWS-Warnings have the highest priority of all aural warnings and thus will supercede TCAS-TAs/RAs.
We had a set-up in the SIM where you are level flight, quite low altitude (~ 2.200 AGL). An intruder descending from above sent us into a TCAS-descent. The fixed TCAS-descent-rate of 1.500 fpm lead to a (E)PGWS-Warning shortly after establishing the descent.
After some brainstorming it makes sense to me in so far as there's a chance you miss the other traffic while you would hit the ground for sure.
Regards, MAX