If you have valid nonimmigrant status, such as an H-1B or L-1, you may travel on your H or L while your adjustment application is pending (assuming that you have no other immigration issues). If you do not have a dual-intent status, or if your status has lapsed, then it is most likely that you will need your advance parole before leaving the US. You should make an infopass appointment at the local office as soon as possible (see uscis website for details) and request an expedite. The expedite...