Yes, at your peril.
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You may certainly do so at your own peril, and risk not being admitted upon your return.
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
I always advise my clients not to travel unless absolutely necessary. When dealing with government bureaucracy it is best not to complicate matters.
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If you travel on the AP and your case is denied, you will be stuck outside the US with no way to re-enter.
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