I think no.He should apply EAD

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.