"Our" TCAS will inhibit increase descent commands below 1500ft, descent commands below 1100ft and all aural alerts below 1000ft. However, all TCAS alerts will be inhibited by GPWS and windshear warnings. There is a priority order, and TCAS is pretty low as another traffic might move, the earth will not.
Added to that at least one pilot should display EGPW information on his ND which will give additional situational awareness. In the situation above even in IMC i would follow the RA as i still have terrain protection while it is active.