You can, but

I think you mean "your company said you were NOT qualified for medical leave", so you have to use adminitrative leave.

The difference is that with medical leave/family leave, your job is guanranteed for three months by law. With adminitrative leave, they can terminate you any time.

However, since you are taking 4 months leave, it doesn't make much difference. They could terminate you after 3 month's medical leave.

It's all between you and your employer, until you are terminated. Then you lose your H1