They do not. So far, I believe all SDS has stated is that they intend to add rewards at some point, once the game mode is more on its feet. That being said, we haven't seen substantial improvement in the game mode through game updates since launch. Some days are okay for playing, some days are bad.
Further, you only get PXP boosts from the host. To explain what I am saying: If player 2 contributes a Mike Trout that is superfractored, but the host does not have Mike Trout, Mike Trout in Co-Op will not be superfractored. If, however, the host has Mike Trout and he is PXP level 3, Mike Trout in Co-Op will be PXP level 3. If that player 2 were the host instead of player 1, then Mike Trout would be superfractored, regardless of what player contributes him.
It is certainly funky right now