i havent tried this myself, but i suspect you wont be able to adjust the brightness as much as you'd think. the cathodes have to run at a very high voltage, thats where the inverter box comes in, and if you start messing with the input voltage, i think the cathode will just shut off before it starts to get to dim.
i could be wrong, but thats what i would expect. and as ben said, it will greatly shorten the life of the cathode.