Ur question is confusing!

I am assuming you are asking in the case your F1 expires before the H4 get arrpoved, right?

If it is a small gap, say a couple of weeks, it is OK. If it is over 2 months, No. In between, gray zone. You need to maintain your legal status before you next one is approved. [Only exception is the extension, like H1b, you can stay once you get a recipt. But this doesn't apply to you, since you are changing from F to H. ]