Do I have to register for the co-op class or can I just skip it?

It depends.  Enrolling in the co-op class allows you to retain your student status while you are gone.  This can help you keep your financial aid, scholarships, and health insurance.  You can also use the credits towards your degree requirements as technical electives or free electives.  

Your next step is to check with Financial Aid to see how the co-op will impact your situation. They can help you determine if you should be taking the co-op class and if you should take it for one or two credits for financial aid purposes.  In most situations one credit will give you part time status and two credits will give you full time status.

If you are here on an F-1 visa then Career Services recommends you register for co-op credits during the summer as well.  By registering as a co-op student you are considered a full-time student and will not be utilizing your practical training time.