Ren is not allowed to touch the crystal. He is also not a team player. If Poe and Ren are anywhere near each other, they're going to try and murder one another.

How do they win this, again?

ANYWAY, Ren is going to want to go off to hunt the objective immediately and will absolutely try to take the lead role regardless of objections from Poe. He won't necessarily discourage anyone from tagging along with him, though! He's a grumpy and ornery sort, but since there's a clear objective and something to gain, he'll be just a tad less inclined to immediately cut down potential competition on his own team.