Most Strats have a small-radius fretboard, and that never stopped anyone from tapping. It can cause strings to 'fret out' on really severe bends. Either problem can be addressed with an appropriate setup. Spend some time with your tech, discussing what you expect from your guitar. If they don't want to take the time, take your axe somewhere else. A setup is as individual as a pair of gloves, and it should fit you that well.