Is Auto Pilot capable of performing TCAS resolution advisory?
Short answer is no.

First of all it is resolution advisory as you said. Its purpose, is to make the Pilots aware of an imminent danger/conflict. As with 'Terrain, Terrain', 'Pull up!, Pull up!', it is up to the pilots whether or not they will follow the instruction (normally they always do, but there are exceptions). 

However when the pilots hear 'Climb, Climb' or 'Descent, Descent', or another TCAS alert, they should immediately initiate the required action. After all, these days there are top-notch ATC and confliction prevention systems, as well as high-tec TCAS systems on most of the commercial aircraft.