The answer is “Yes”. If you check your I-94 (the small slip given to you at port of entry when you entered USA), your authorised stay in USA is “D/S” which means “Duration of Status”. In other words, you can remain in USA till you maintain status of a student. The condition of maintenance of status under the first I-20 was that you were required to take up certain credit hours of your course and not to take up unauthorised work. When you completed your study, the status ended but the same was extended by issue of a new I-20 based on which you applied for OPT Employment Card. This time, the condition of “Duration of Status” was that non-employment should not exceed 90 days. The moment there is non-employment of more than 90 days, or the date mentioned in OPT expires (whichever is earlier), the student becomes out of status and the grace period of 60 days begins. Now at this stage, if you get a new I-20 till June, 2013, your status as student continues till June. But, there may be a few complications : (1) If you know that your name is not selected in lottery (i.e. your H1B petition is returned before you apply for new I-20), then obviously you cannot even apply for new I-20 (2) If lottery result of all the petitioners is out before a new I-20 is actually issued to you, DSO will insist upon proof of your petition’s selection.
(Note : Even those students, whose H1B petition is selected in lottery, have to apply to their DSO for I-20 “cap-gap extension”, if their OPT would expire before they get their H1B visa).
(Note : The earlier disclaimer applies)