Yes, and yes. Your S can either apply to LSA or CoE for CS. There’s small difference in curriculum, but you can obtain a CS degree either through LSA or CoE. CoE will be a bit more difficult to gain acceptance than LSA, since there are fewer spots available in the CoE (4,200-ish vs. 1,200-ish):
http://www.eecs.umich.edu/eecs/undergraduate/cs_lsa_vs_engr.html