If you have residence permit for family reasons (old 'L' visa). You can study. I have also studied whilst on a 'Z' visa. This was acceptable to the university administrators.

However, if you try to work or do business on a student visa, you are highly likely to get bounced. Student visas are monitored very closely. I have heard of people who missed only 3 classes (one guy because he had a weekend trip away with his gf) not being able to get the student visa renewed.