申请OPT is always OK lah since your are F-1 and not H1 yet.

but what's the activate date of H1?

as far as I know, two application,the last approved will be the final status.
so in this case, if your H1 got approved fisrt, I don't know if you need to cancel your application for OPT.

The best thing is to ask the international officer or call a lawyer and get some idea.
aND SINCE he applied for H1, he may ask the lawyer who did H1 for him.
Those are professionals.