[quote=@Dead Cruiser]
This is probably a stupid idea but I'll throw it out there anyway: assuming I put up the Enterprise, what if they had a stowaway? That is, the entity known as Q having hitched a ride to this universe, and planning to screw with the others for his own amusement. 
[/quote]

I'm going to say no to Q cause there's enough going on already. I'd also argue an entity such as Q wouldn't have to stowaway if he really wanted to crossover. From what I know he's basically an ascended being.