I started scribing the semester I took physics 2, and 4 upper level math classes. I worked part time that semester, which is 2-3 shifts per week (at least 12 per month). After I graduated, I worked for the company part-time, but only on the weekends, since I also had a full-time job during the week. I am also extremely skilled in time management (sorry for the humblebrag, but it's the truth). Here are some thoughts on the experience:
While in school:
Difficult to manage, but definitely possible. I am very type A and I like to get A's, so there's that to consider, and I do think it would have been much more manageable if I were OK with B's. Personally, I feel that the shift work is the most difficult part, because your class times won't change, but your shifts could be scheduled in the morning one day and overnight a couple days later. That said, you have a good amount of control over how you deal with it. You get the schedule for the month about one week in advance of the 1st of the month, and your syllabus should be relatively set, so you can schedule studying around your shifts, since those shouldn't change unless you're kind enough to switch with someone or your scribe company has an on call system. You might be tired and distracted at times, but there's really no reason to fall behind as long as you schedule time for school.
After graduating, while working full time during the week:
I wouldn't recommend it.
I would also consider how many shifts per week the company quotes you. If they say 2-3, realize that it is an average and there will be crazy weeks. For example, around finals and around the time people submit primaries/take the MCAT, you could be the lucky grunt who gets 7 shifts in a week (I'm not kidding). They'll tell you it won't happen, but just keep in mind that it can and does and we all took turns being that person. Planning ahead is crucial.