If your case gets denied while you are outside the country, your AP is effectively cancelled and you will not be allowed in. Also, if the BP agents find a reason to deny you entry they can. Just because u have an AP doesn't mean automatic entry, it's the discretion of the BP agents. Having said that, the risk of getting denied is very low. But immigration lawyers like to give you the worse case scenario to cover their asses.

if you have an emergency you can travel with no problem, I went to brazil 🇧🇷 my mom was very sick, now if you are going on vacation it is little risk!!!