You need to check with SSA about what will happen if you are approved-- there may be some limits on getting payments when you are out of the US.
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You can leave, but you will need to be prepared to return if needed to pursue your case. In particular, if an administrative hearing is necessary you will definitely want to be present.
Best wishes for a favorable outcome, and please remember to designate a best answer.
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The process itself does not restrict your ability to travel but you may want need to come back for a hearing. The vast majority of my clients need to appear before an Administrative Law Judge to testify. Best of luck to you.
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