It's all going to come down to what size tires you can stuff under those front fenders. Rear grip is rarely an issue in Stock class autox (unless you're running a Viper/Vette or an S2000), so large enough rear tires will likely be able to fit just fine. If you can stuff a 225 Hoosier under that fender (highly unlikely), watch out! If that's the case, the Elise will be a terror in Super Stock...at least until we see what the C6 Vette will be like.
However, if, as some have speculated, you can only fit a 195 or so on the front, ultimate grip may be at a slight disadvantage. We also need to consider the availability of tires in an R-compound. If it's not possible to fit a nice-sized 205 on the front, there may not be any desirable options for front tires. That would be a shame, but something that I know several people are in the process of investigating.
If the car only fits 205s, I would think that A-Stock might be a decent fit (although the Elise would likely still dominate). Unfortunately, the Solo Events Board has (with a few notable exceptions...the Evo8 in ESP comes to mind) been pretty conservative with their classing lately (ask RX-8 owners about this). Given that, I can't see the Elise being initially classed anywhere south of Super Stock. However, even with narrower front tires, an Elise should be able to, on most courses, give the Vette Z06 a big run for its money.
Final note: given that the specs and options for the US Elise are not even yet finalized, take the above as a complete guess.

In addition, unfortunately for those that would purchase an Elise without the sports suspension, they'll likely be classed in the same class as those that DID opt for the upgrade.