Is it true to always test the air bleed valves on the radiator when inspecting a boiler?

Not necessary. If a boiler system is operating properly there should be no need to test the valves.

I would also like to add that any time a boiler has air introduced to it the valves will then need a bleeding. This can happen at anytime fresh water is introduced into the system.

I would also like to add that if you open a air bleed valve when the boiler is cool on many systems this will cause air to be sucked into the pipe due to the lower pressure/no pressure of a cold boiler. This can cause more problems when the boiler fires over.

Stay away from the bleeders unless they need to be opened to remove air.