This is an old thread but now that I have a few events in with the car I can add something:
I'm using a Cooper CVT (in H Stock obviously) this year in Brian's SCCA region. Surprisingly to me, I'm doing better than the rest of the local class including some other Coopers with the 5 speed. However, I think that's probably because: 1) I have a year and a half of regular autocrossing under my belt and I believe my competitors are not as experienced, and 2) I'm running Hoosiers and they are not.

I have no idea if I would be faster in a 5 speed, although I'm coming from a 5 speed twin turbo RX-7.
Anyway, I like the CVT for autocrossing (and on the street), but the real weakness is getting off the line. For this part, I do the 1-D-SD "flick" that has been discussed elsewhere on the forums. For the rest of the course, I think the CVT does a great job of keeping the revs up in SD. I haven't tried left foot braking in competition yet, as my brain just freaks out when I have tried it in practice. In any event, I'm not sure if the computer lets you get the most out of this technique.