Can a doctor’s note stating an employee is permanently disabled be enough to terminate an employee

The issue is not the doctor's note per se. The issue is:
1) If the employee has exhausted their FMLA, have they returned to work? If they have not, and also do not have PTO remaining to cover any absence, then they can be terminated for absenteeism: an employee may only miss work for an alleged medical reason when using FMLA and/or PTO.
2) If they have returned to work, they must be able to do their job--you don't have to provide "light" or "reduced" duty or give them a different job. If they can't safely and fully do their job, you may terminate them. The most you might have to do is to make "reasonable accommodations" to make doing their job easier, if such accommodations are not too expensive or disruptive. (Examples include: if an employee like a cashier normally stands, but could do her job sitting, allowing her to sit and getting her a stool; getting an employee who suffered hearing damage a phone that amplifies sound; letting diabetic employees take frequent short breaks  to test blood sugar or have a snack to balance their sugar.) But the employee must be able to do the important or core functions of his or her job
So what the note says doesn't really matter: either the employee comes back to work or does not; either the employee can do his/her job or cannot.