No, you pay a few small fees (my guess is somewhere around $1000, maybe less) to maintain status as a student because the co-op is a 1-credit class for that term. You have the option to pay out of pocket for any other classes you may want to take that term (many of my friends took a night engineering class to get some electives/etc. out of the way while on co-op in the city).
For the term you are on co-op you can request a hold on all of your scholarships. Most scholarships run 8 semesters long. It does not matter which semester you use these for. That is, if you co-op in the spring and then take classes in the summer, you can apply your scholarship towards the summer term.