No, ArmA Edit has not been updated to use Arma 2's new briefing style. That has to be coded in SQF. All that briefing.html files are used for now are the debriefing messages but, unfortunately, BIS have kept the game looking for the briefing.html file at the start of a mission in order to show the briefing before the mission begins. Therefore you need both a briefing done in SQF and a briefing.html file only containing the debriefing messages for the briefing to work properly.