No, EF-S lenses cannot mount on full frame bodies - they will only work on crop-sensored bodies.
However, EF lenses are compatible with both crop and full frame bodies.
My #1 rule of lenses - always buy FF compatible. However, if I were more devoted to Canon's line of APS-C sensored bodies, I'd seriously consider the EF-S 17-55. That is a beast of a lens!