Voltage clamping for nixie tube driver
Unless you use absurdly long wires (as in feet or yards of the stuff) to connect up the circuit, no, inductive effects should not be a problem.  You're probably thinking of relays, which need an inductance (the relay coil) in order to work.  Nixie tubes aren't appreciably inductive.

All gas discharge tubes, when they are on, are basically constant-voltage devices.  And to complicate matters, they need more voltage to turn on (the "strike voltage") than they need to stay on.

So you want to do something to limit the current to the tubes.  If you were to just connect them straight to that part then you'd fry the tube, the part, or both.  It's likely that the part would die and save the tube, but you couldn't count on it.

Connecting all of the anodes to your +V should work fine, but you want to connect the cathodes to the pull-downs through resistors, whose value is set to get you the rated current through the tubes.