No. (Read more)
If your EAD for OPT expires on Feburary but you have to wait till March to file for your H1B, you have to ask your attorney to file an application for B2 visa (visitor) visa before the expiration of your EAD(OPT) to keep you in status for the few days before you file your application for H1B.
Please talk to your attorney. I think it is doable.