I'm thinking of changing my string gauge from .011-.049 to .013-.056. My guitar is a Squier Stratocaster, made in Japan. The truss rod will probably need adjusting (it didn't when I went from 9s to 11s, but this is a bigger change), but what about the tremolo/vibrato system? It currently has 3 springs, will I need to add more to counteract the increased tension?
yes. you need to set-it up properly, meaning the truss rod, action and everything. if the bridge raises, add more springs to your trem.