I do not smell coolant at allif your coolent is low there's a good chance the radiator plastic end tank is leaking somewhere. if you look for it while it's hot, you can probably find a wet spot. leaking water doesn't set a check engine light until you've overheated it enough. usually by the time is comes on its hot enough it's not good for the engine at all. if it is leaking you probably should be able to smell the coolent.
the price seems high to someone like me that doesn't go to shops, that's about 200-400$ in parts. but the diagnosis seems plausible and having cars fixed is expensive. you could get a 2nd option from another shop and ask them to show you the leak.