Yes on some cars the coolant level being too low could cause the check engine light to come on.
Most newer cars have a coolant light as well that tells you if your coolant level is low and needs topped off.
Your engine temperature could also increase if your coolant level is too low so watch your engine temperature as well and if the engine starts to get too hot then you need to pull over, shut the engine off and allow it to cool for 30 to 50 minutes.
Then open the coolant reservoir cap or radiator cap and check the coolant level and if it's low you need to add some more coolant to the system.
If you're constantly loosing coolant then you should check to make sure it's not leaking into your oil or it could be leaking out of hoses and gaskets.
In a properly working coolant system the coolant should not be lost all that much.
Losing just a bit of coolant over 5,000 or so miles of driving is normal but you shouldn't have to add much coolant.