Reverse polarity will at the very least cause uneven wear on the electrodes. One is designed to be a cathode, and the other is designed to be an anode. If you switch their roles, tube life will be reduced. The clearance on the cathode to ground may also be insufficient to handle the high voltage (the cathode is typically grounded at the PSU, if memory serves), potentially resulting in flashover. Basically, the tube would crack and the PSU would shit itself.
You can safely operate the tube without water for about a second, if you leave it off for several minutes between firings.