Is it cool to marinate chicken livers over night?

I don't know but you can hedge your bets by skewering the chicken and setting them in the marinade. How about testing a small sample first? Make a batch of marinade and see what happens with 2 or 3 livers at a time. That's something I do when I'm writing recipes for my cookbooks.

Also, use livers on the largish side.

Will these fall apart if I try to skewer and grill them?

There are rumaki recipes that call for marinating whole chicken livers overnight so it seems like you'd be fine to do that. You may not need that much time if the livers are not super livery tasting.

I marinate them when I'm making pâté, but not otherwise. They would fall apart/crumble when you cook them.