Not important at all. If you don't want your car to ding at you on every start and require you to hit OK in order to see the information screens, it's necessary.
Won't affect traction control, stability, warranty, etc.
Out of curiosity I have to ask:
Why fight to fit a 10" wheel all around, potentially not have the center caps fit, and only throw a 275 on them:confused:
I'm pretty sure EB/PP brakes are the same as base GT, which come with 18s standard. I'd do the extra 18in wheels instead of mounting and remounting to the 19s. Check the classifieds here for some cheap stock 18s. Might be less than the wheels on Tire Rack.
While shopping, I recommend you pay particular attention to tread wear rating and price (i.e., a slightly higher price for a higher rating will probably be more cost efficient in the long run).