I am taking a SW class at a local community college now and we can take a SW certification test as our final exam. We have the student software. So I would assume that you can, and that what we are doing is not some special arrangement between our school and SW. It would be stupid if you couldn't since the main purpose of certification is to land a job. Most people wont have access to a full version without getting job.
I have heard of people wanting to get a certification that went to a VAR to use their systems to take a test. That way they could become more marketable and didn't have to take a class or purchase any of the software; student or full.
Student version is fully functional - only the terms of license are different.
You can use to complete the Certification exams.