You can stay here without stamping after your H1B is approved for approval date authorized in H1B. If they are sponsoring your H1B then I don't think they care you are you in OPT F1 or foreigner that is what H1B is meant for.Just make sure you graduate in time with all requirements met and you can work with them in OPT ( apply that in time as well after graduate) and later work with them on H1B once that is approved.Hope that helps.