I have a 2016 chevy cruze 4 cyl that has a head gasket leak and won't start. Is it possible that there could be engine damage if the car won't start?
You can't drive a car with a broken head gasket.
Sure you can, the question becomes how long will it last. I once test-drove an Astro van that the guy admitted he had to pull a plug and crank over to blow the coolant out but once he did that it would run, kind of, on about four cylinders. I actually tried to abuse it a little so it would blow up so nobody would buy this piece of junk, but no luck.
As for the OP's car, there's no way to know without looking inside. If it cranks over and just won't fire, it may be okay. And if the coolant is just in the cylinder and has hydrolocked it, that might also not be terminal. But it depends on how the gasket failed and where the coolant went as a result. if it got in the oil and you drove it that way, then the bearings are likely damaged. You can check the oil for a milky substance inside the cap, or oil with the consistency of a chocolate milkshake.
If the oil and the coolant are fine, then you could be okay. Well, relatively okay, the head still has to come off and the gasket be replaced. Hopefully it didn't fail due to overheating, then the head itself could be warped. I don't know if a Cruze has aluminum components or not.
So the bottom line is check the oil, check the coolant, if you're not a mechanic I don't know if you can do much more yourself on this car.
I know that those engines do have aluminum components and most likely did overheat. I am going to assume the head or block are warped and possibly have additional damage. Thanks for your help