Travel while adjusting status must be done in accordance with stringently enforced restrictions (i.e. advance parole, in certain nonimmigrant visa statuses, etc). However, if done correctly, traveling while adjusting status is not an uncommon occurrence.
So what happens if you are traveling overseas when your AOS application is approved? According to recent Customs and Border Protection commentary, a person should provide the approval notice of the adjustment of status application to the immigration official at the air port or border. If the individual is able to provide the approval notice, and the CBP is able to verify the AOS approval in their systems, the CBP will allow the entry applicant to enter as a permanent resident.
Of course, there is no assurance that an individual immigration official will know the CBP’s policy. Contact a knowledgeable customs and border immigration lawyer before trying to enter the United States in an uncommon situation.