this is just paranoia!
Among all the great, wonderful, fantastic information available on this forum,
this is one thing I do not like about this forum - when it creates paranoia like this.
In this case, when paranoid users convey that you cannot travel just because you have received an email telling you that your case is approved:
1) What proof does USCIS have that you have received
and read your email?
2) AP is meant for being able to travel outside the country without abandoning your application for adjustment of status. What logic tells you that using it after it is approved, will abandon it?
3) There are posts from users that have entered on AP in such scenarios without any problem. There was only one where the person was asked if he was aware that his case was approved before he left. He said that he was not, and he was let in with a deferred inspection.
4) There have been cases where users have got approval emails, and later found out that the email was in error. If you read the terms and conditions of the USCIS email notification system, you will know that it absolves itself of any errors. So, there is no way to rely on emails as 100% proof that your case is approved. So, if you are asked if you were aware that your case was approved - you can truthfully say : "No"!
I quote from
https://egov.immigration.gov/cris/jsps/termsconditions.jsp?contextType=CU_EN :
Accuracy, Completeness and Timeliness of Information on the Site
We are not responsible if information that we make available on this site is not accurate, complete or current. The materials on this site are provided for general information only, and any reliance upon the material found on this site will be at your own risk. We reserve the right to modify the contents of the site at any time, but we have no obligation to update any information on this site. You agree that it is your responsibility to monitor changes to the site.
5) What proof would the CIS have that you have received your approval notice, until you walk in for a stamp. Surely, you cannot wait for months between your approval and stamping and claim that you did not receive your approval, but if its a matter of days - come on!
The bunch at the CIS maybe a crabby bunch, but they are humans. They may seem like they are out there to get you - but they cannot stretch the rules to such an extent.
Having said the above, I do want to absolve myself too - this is my personal opinion. This is not communicated to me by an attorney and I have not specifically read any rules. I do know this: If an officer at a POE stops you from entering as a permanent residence because you left after finding out that your case was approved, there would be a lot more to it. I would be willing to bet that the officer would have many easier tools at hand to stop you. They are not going to call for trouble by being unreasonable like this.
So stop worrying and have a safe trip!