2007 Grand Prix overheating

Yesm but looks like there might be a crack in the lower intake that someone tried sealing with RTV before. That line down the right side of the right hole, heading towards the block. Even with fresh o-rings on a new elbow, you'd probably see leaks there, along with a possible vacuum leak from air getting to the crankcase.

Replacement/repair isn't too involved, once you get some gaskets, RTV, teflon tape, and a new lower intake from eBay, classifieds, or a yard.

If the elbow is missing, you will have no coolant flow and will overheat quickly. I would put that in asap. Easy install. Remove the alternator bracket and install new elbow from ZZP. This will be the only way to tell if the possible crack is also leaking.