You can indeed coop all missions available in game so far. 

I would suggest checking out the first Developer stream done by Neocore recently for Inquisitor Martyr as well as Hydra's videos to see more on exactly what we have and don't in game currently.

Hope to see you purging the system soon fellow Inquisitor, good hunting to you.

no you can't tried it with a friend of mine since 3 weeks we can't play, always got the "server timeout" message, pure garbage at the moment.