getting an AP and using an AP are two entirely different things. Using an AP means going out of US and showing AP to enter the US as a parolee instead of showing the visa to enter the US as a non-immigrant. As parolee can't work in US, he/she should get EAD before traveling on AP. Receiving AP is just addition of one more document in your file.
So just receiving EAD/AP does not change the non-immigrant status in any way and he/she is still on H or L status. Thus the person is either in EAD/AP status or in H/L status.
As long as the person maintains the H/L status(H/L status not expired and H1/L1 holders not working for any other employer other than sponsoring employer and H4/L2 holders not working at all), he/she can travel outside US and come back with out the need for advanced parole even after applying for adjustment of status. The person can enter using his/her non-expired H/L visa. The person needs to carry his/her "original" I-485 receipt otherwise serious delay at the airport may be caused. For valid H/L visa holders, there is no need to apply for EAD to continue working after coming back to US.
