In Tel'aran'rhiod, the dream becomes what you believe. Mat believes he is lucky, so combined with his "luck" ability, and him making himself lucky, he would be incredibly hard to hit with anything. He might just get "lucky" and the person's heart would stop or their ball of fire would hit one of his enemies. Having the memories of old generals have taught him concentration and focus, making him more prepared for Tel'aran'rhiod. Many victories in the world of dreams have been surprise attacks, or unexpected moves. Mat's double luck would make him perfect for executing and avoiding these tactics. Of course, he would have to have a ter'angreal ring that would allow a non-channeling man to enter Tel'aran'rhiod or learn to dream into Tel'aran'rhiod. With Perrin to teach him, I think Mat could become a god in the world of Tel'aran'rhiod.

Mat's luck isn't something he can consciously control.  And a good part of his luck comes from being ta'veren, which he no longer is after MoL.  His luck, whether good or bad for him, serves the Pattern and whatever place it has for him.  Having a building fall on him was hardly "good luck," after all.  But it is just the luck he, and the world, needed to keep him in the place the Pattern needed him to be in.

Honestly, Mat would probably be horrible in T'a'R. To be strong in the dream one has to be extremely focused and self-aware. Mat is neither of those things.