To my knowledge, online games are still Adventurers League-legal, so long as you're playing according to the AL guidelines. The exceptions to this are D&D Encounters and Expeditions, which (as I understand the AL Players Guide) have to be streaming. So Twitch, Discord, Google Hangouts, and Roll20 would count as legal but play-by-post wouldn't.
But for just playing the AL adventures, play-by-post seems to be AL-legal.
http://dndadventurersleague.or...-adventurers-league/