I had the interview for adjustment of status 3 weeks ago based on marriage to an American citizen. Immigration official said will send results by mai.

It is risky traveling to Ecuador at this stage with advance parole. You could have difficult few-entering if your application is denied. If approved, sending a green card is risky as it may get lost. Have you tried checking your receipt numbers at www.uscis.gov? If your application has been approved, you could obtain a stamp in your passport that is proof of residence. You may want to consider an infopass appointment at the office where you were interviewed if no decision has been made.