It's doable. The company I work for is fairly sensitive to school schedules. Right now, I'm in school over the summer and working as a scribe and EMR tutor at different hospitals. I've probably had about five hours of sleep over the last two or three days. This isn't normal, and during the regular school year I only work as a scribe, usually on weekends, but there is the occasional night shift before a test/quiz. But during these seasons, caffeine becomes your best friend. I just consider it as residency training.
I'm actually working a night shift right now as an EMR tutor. I'll get off around 7 am or so, go home and sleep for an hour or two, and have class from 10 am to about 3 pm. I'll grab a bite to eat and head off to work as a scribe at a hospital about 45 minutes away from my house from 5 pm to 1 am. Then I'll have the blessed weekend off....
Edit: I will say, however, that despite the occasional craziness, I thoroughly enjoy scribing and have learned a ton. I definitely feel comfortable with patient-doctor interactions, have picked up a bunch of medical terminology, and was able to get some great LORs from three doctors that I have worked with for about a year. I would definitely recommend it if you have the time and are able to do so.