No, you can't I fear. Mechanics and basic engine systems are likely not changable with the editor (outcome of the AMA). And you would need a sort of matchmaking system and a system which would allow real people to play against each other.
Would be mucht better to have a PvP mode from the beginning (or in a patch/update later?). As I said, it's also a strong marketing and sales argument because it would be a complete new game mode (without THAT big effort of Larian I guess).
The fighting against eachother is probably already covered, you can harm eachother and if you can put people in different factions ("teams") you're already most of the way there I should think. I guess the difficulty would be to split the teams up (though it *could* likely be made to work with everyone in the same party) but that would also require UI changes, especially if you start talking about stuff like 1v1v1 or so. But if anything needs to be added to just allow PvP it could probably be done with relatively minor effort I'd think.
Personally my only interest in PvP would be to fight out who's build is best (you just *know* this argument will come up sooner or later) in a sort of controlled environment, being able to guarantee people start the fight on equal terms (take away consumables etc for a match, maybe lock out henchmen, yadda yadda), there's no need for matchmaking for that and I'm pretty sure implementing matchmaking isn't exactly a minor undertaking so personally I'd rather they don't bother with that aspect. Also as soon as matchmaking etc comes up I hear competitions, ladders etc sneak in and...meh just meh, not interested.
Either way without actual input from someone of Larian we can't really know how much can be done with the editor as is and what would require extra effort to make it possible.