If I had to guess, I'd say no. I think part of the reason for the altered timeline/quasi-reboot/prequel is so that future films can focus on something new and unexpected, something we haven't seen before. At least, that would be my hope.
If this were a TV series done in the same fashion, then I'd imagine that they'd probably do that every so often though. In that medium, it might be kind of neat to see a NuTrek take on some of the original series episodes. But for these new films (assuming there'll be more), I believe the idea is to break away from the Trek canon of old (which had arguably gotten too cluttered and constricting) and create a new one -- rehashing old concepts and stories is probably not the best way to go about doing that.