If you were smart, you would tell the shop to not try and start the engine.
Just pull the plugs and crank the engine over to purge the cylinders.
Put plugs back in, top off oil and start the engine. If the engine starts, you need to pick the car up and drive it for more than 1 hour on the highway and check the engine temp using the Hidden OBC menu.
If you have not been making a lot of short trips, you likely need a thermostat as well??
CCV likely needs replacement, however, I think coolant temp and short drives is a bigger factor than the CCV itself.