My greencard application is currently pending (I have an F-1 student visa and was married to a US citizen last year). I am hoping to travel internationally during the 60day waiting period. I have an advanced parole document. If for whatever reason my application is denied (while I am abroad) will I have trouble re-entering the USA? thanks so much for your help.
If your Adjustment of Status (AOS) application is somehow denied while you are outside the country, you will probably not be able to return. Normally, if CIS denies an AOS, they also deny any underlying applications such as the Advance Parole (AP). You may also have a problem trying to return using the F-1 visa (if it still valid), because F-1 holders are supposed to have nonimmigrant intent, i.e. they are not supposed to intend to be permanent residents. You obviously contracted that intent by filing for permanent residence.
It is unlikely that your AOS would be denied without an interview. However, there are other factors that might affect your ability to travel, including your prior immigration history and whether there were any status violations or overstays. I recommend that you speak with an experienced immigration attorney before travelling anywhere.