I think the only ohm test you could perform on it would be to ohm out the heater filament. Again, this is really only to tell if a heater would light up, and doesn't tell if all heaters are good nor emission.
The CRT tester is really the only way to test if the CRT is good --and of course seeing if it will hold a good grayscale, and color picture without looking chalky, or defocusing even though voltages are normal.
The tester puts a small amount of current between the gun elements. The amount of current measured in micro amperes is the gun's emission --or at least a way to measure it. More sophisticated testers will detect grid leakage or gassy tubes. How they do that exactly varies by manufacturer --and quite frankly I don't know
