Well, if they're cut really thin, I certainly wouldn't marinate them overnight. Depending on the contents of the marinade, you could break down the proteins to the point that your meat is mush. Furthermore, it's just not necessary. If your goal is to infuse the meat with some flavor, you don't need that long for very thin cuts. I'd just marinate them for 30 minutes or so, just before they go on the grill.
Best,
Michael