With Sins 1.191/Entrenchment 1.051/Diplomacy 1.011, the AI does use some ultimate abilities on capitals. Mind you, it usually just uses the ability whenever possible, so it's rarely the best use of the ability. Example, I've seen an enemy Rapture Dominate one of my light carriers, the next (and last) Domination it got to use was on a light frigate. So, the selection seems to be whatever appeared first/is in range/is closest.
I've seen the AI use Domination, Volatile Nanites, Stabilize Phase Space, and Disintegration. I haven't played against a TEC AI enough recently to see them use ultimate abilities (usually, other AIs kill them and/or they all random to mostly Vasari/Advent).