My understanding is that students have to be enrolled in a course before they can be allocated to a group. And no, don't change the default role to student. This is rather bad (I can't remember why) and will lead to a lot of unexpected side effects.
Why not enrol the students into the class and allocate groups using the batch uploading? I'm sure it's possible to enrol a student in a class who you have already uploaded (if you see what I mean). Check out this document:
http://docs.moodle.org/en/Upload_users
General help
auto create groups + roles
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