Since you want to apply for an H1-B, I assume you already have a job offer - good for you.
When the employer applies - on your behalf - the H1-B, the company needs to justify hiring an international for the position. As long as the company can do this, all is well.
I think if you continue to register for classes, your F-1 status should be fine. However, have you considered applying for EAD (optional, not curriculum) for the position instead?
As you know, with EAD, you can choose whichever company you want to work for. With an H1-B, you can only work for the company that sponsors your H1-B.
When the employer applies - on your behalf - the H1-B, the company needs to justify hiring an international for the position. As long as the company can do this, all is well.
I think if you continue to register for classes, your F-1 status should be fine. However, have you considered applying for EAD (optional, not curriculum) for the position instead?
As you know, with EAD, you can choose whichever company you want to work for. With an H1-B, you can only work for the company that sponsors your H1-B.