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If you filed an I-290B, you would be placed into a stay authorized by the Attorney General. If approved, then you could get into F-1 student status without having to leave the U.S., however, if it is denied, your unlawful presences counts from the date that your I-94 expired or your change of status to student visa was denied (whichever is later). If you reach 180 days of unlawful presence, you cannot come back to the U.S. for 3 years after you leave unless you get a very hard to get waiver. It is 10 years if you reach 1 year or more of unlawful presence.
Unless you have a VERY good reason for USCIS not receiving your package in time (that you forgot, that you send the wrong money, or anything like that is NOT a good reason), then I would STRONGLY recommend leaving the U.S. as quickly as possible because the faster you leave, the easier it will be to convince a visa officer when you apply from outside that your overstay was brief, reasonable and won't happen again.
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