I've been to group interviews where they pretty much do that. Randomly divide all the candidates into groups, give them a task, see how they work together.
I can't say I enjoyed the experience - and I've no idea how good it is as a tool - but it was illuminating to see how people treated each other.
You'd be better off arranging to play a strategy, preferrably collaborative, boardgame.
One day I'll use Pandemic as an interviewing tool. I wonder of it'd work as a pre-formal interview stage