You should contact the MAVNI office and make the inquiry. Under the guidelines, your status has to be current under the various categories, nobody can tell you whether grace period counts except the MAVNI recruiters.
You need to at least be in lawful status in order to be able to be considered for the MAVNI program. You can contact the Armed Forces and discuss your situation . Good luck to you.
When you attempt to enlist under the MAVNI program, you will be asked to provide immigration documents showing that you are in lawful status, and the recruiter will check those documents with DHS using form G-845. The G-845 check can take quite awhile, and so can the enlistment process. If you are in your grace period, it's theoretically possible that you will "pass" the G-845 check--but it can take a long time to complete the enlistment process. The SSBI (Single Scope Background Investigation) takes about six months, and you cannot go to Basic Combat Training until you complete that process. If your grace period has expired, and you fail the SSBI, you will have violated your immigration status and will likely have to leave the United States. So it's not a good idea to enlist while in your grace period unless you plan to change status to H-1B or go back to school or otherwise extend your status. Many recruiters won't allow you to enlist if you are in your grace period for this reason. But it's really up to your recruiter. Theoretically, it's possible.
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