In general, 17" combos weigh more and carry their weight further out on the rim so they have a larger polar moment. Net result, slower acceleration. At the same time, 17" combos have a larger diameter in most cases and will make your gearing effectively taller. Net result, slower acceleration again.
I would recommend that you stick with the 16s for autox, and if you have a dedicated set of street tires, use 17s for those instead.
All of the local STS guys here in the SF Bay area use 15s or 16s. I myself use a set of lightweight 15s with 205/50-15s for autox, and the stock 16s on the street. The RSXs use 16s for autox and 17s on the street if they have dedicated race tires.
You MAY see slightly better cornering, but your acceleration, braking, probably cornering, too will be reduced with 17s. If you get the right tires, the potential disadvantages of taller sidewalls for the 16s will be more than offset by the tire capabilities.
Most of us run on Falken Azenis tires for STS or Kumho Victoracers or Hoosier R-compund tires for stock or other classes. These are examples where the smaller rims will most likely perform better than the bigger rims.