Not every school offers incompletes.
In our experience, there was a dean or other administrator who told professors what to do in these situations, sometimes in no uncertain terms. They needed to make sure professors didn’t violate the Americans with Disabilities Act, I assume. The dean insisted on an MD documenting the issue, that that was all. Professors did have some discretion but overall, they had to accommodate- most were great about it anyway.
My daughter had chronic health issues in college and took two medical leaves. To be honest, both were fantastic experiences: she made them into coop semesters, I guess you could say. They energized her schooling and her goals. That said, she graduated a year and a half after her peers (with reduced course load the last year).
Same daughter went off the grad school and got mono the first month. The mono attacked her cranial nerves and she was cross-eyed, couldn’t see well. (I asked about corticosteroids and not a single MD thought they were a good idea.)
The thing about mono is that you start to feel better, and take some course or activity back, and then relapse. It is a tricky recovery. My daughter’s school too her off all teaching, then she felt better, started teaching again, and got worse. Even after a few weeks of feeling better, there would be days when she was super tired.
Once the mono really gets going, it can be bad: you really cannot get out of bed, and mental work is tiring too. However, some people do have milder cases and strong immune systems.
I would consider a withdrawal to preserve his GPA. It’s up to him. Extensions will mean pressure and it is uncertain whether, in, say, two months, he will be able to catch up without affecting his health.
It’s hard to tell though. If he can wait a week, or even 5 days, to see how the mono develops in full bloom, maybe he will be able to tell if he should leave. But in the meantime, schoolwork backs up and if he is a kid who works hard and does well, he shouldn’t suffer a drop in grades- better to leave.
Remember this is not a chronic illness. He will resume his life.