Well, normally at least the cathode voltages are nearly equal, and the impedance of the circuit that sets the resting cathode voltages (from the 3 setup potentiometers is is fairly high) and the output from the R,G and B amps is AC coupled, so linking the cathodes is of no threat to the circuit components or crt. So if there is a signal coming out of one or two channels of the R,G,B amplifiers that is causing the "color tilt" it would be eliminated on the image, even if there was a small change in brightness of the overall crt raster.
I have never had the need to do this myself, because I would simply put the scope on the output of the amplifiers or on the CRT's cathodes (sync's at H rate) to look for a tilt voltage. I thought this idea up as a way to help diagnose it without the luxury of a scope or familiarity with a scope. Yes and swapping cathode connections would also work as the colors would change if it was due to a changing voltage over the H scan time coming from one or two of the R,G,B amp outputs.This could be done swapping the wires leading from the R,G,B amps on the main board to the pcb on the crt socket assembly.
.....if its not a problem in the amplifiers, and it did not alter or improve after using a de-gaussing wand on it, I would wonder if there is physical damage to the shadow mask in the crt....