For the most part, checking the coolant level in the radiator will not introduce air into the system. So don't be afraid to check your coolant levels!
With that said, there are a couple of things you should know. There are (for the most part) two different types of coolant systems.
- Expansion tank - This type of system is basically a closed system. It will most likely have a clear (or semi-transparent) tank which has the pressure cap on it. This circulates the coolant through it and allows a place for the air in the system to be captured. You use the coolant levels in the tank to determine overall whether you need to add coolant or not.
- Recovery tank - This type of system uses a bi-flow radiator cap in it, usually on the radiator itself. This radiator is capable of flowing in either direction. The idea is for the air to flow out through the cap and through the tube, down to the bottom of the recovery (or overflow) tank and vent to atmosphere through extra coolant which is in the recovery tank. This happens as the system heats up (and pressurizes). Then, when the system cools down (and creates a vacuum), it sucks coolant back into the system from the bottom of the recovery tank. Recovery tanks are usually semi-clear as well, which allows you to see the amount of coolant in it and can adjust accordingly.
Please note, some systems still require burping. These are most often ones with a recovery tank on them. Not all will need it, but some will to allow you to remove most, if not all of the trapped air in the system. Yes, trapped air is usually bad for a cooling system, because it can introduce hot spots. Air allows steam to form. Steam cannot remove heat from the engine anywhere close to how coolant can. Keeping it full is definitely something you need to do, but once you get it full, keeping it there is usually a matter of just checking the level in the recovery or expansion tanks, both of which can be done without removing the radiator cap. As long as there's no failures in parts of the system (i.e.: blown hose; bad radiator cap; blown head gasket; etc), you really should have to worry about it.