No. If the leds in each column are indeed being current controlled by a current sinking constant current driver, then the switching transistor does not, and in fact should not have a series base resistor installed. The collector emitter junction of the transistor will be forced into full saturation and will have minimum voltage drop, but even if there was voltage drop the constant current sinking output drivers would compensate and maintain proper led current at all times. That is how my 5x5x5 led cube is wired up using this schematic:http://picprojects.org.uk/projects/lc/Cube555Csch.pdf
Edit: My above my not be correct for your circuit because even though you state:
The output pins that control the columns won't need resistors because they are going into a LED driver transistor IC.
I think that is an inaccurate statement as the ICs you are using for current sinking output are not of the constant current type, but rather just Darlington driver outputs. The output shift registers used in my schematic above do use constant current output drivers to control led current, your circuit appears not to and I don't see how you are managing led current correctly. And just adding a base resistor to the switching transistor will not solve the problem of led brightness will vary depending on how many leds you might have commanded on in any given level. That seems to be a flawed design in my opinion that is just relying on the scanning speed duty cycle to keep peak led current from destroying the leds.