If the two systems are completely independent, including battery, motor, controller, etc., there's no reason it won't operate.
How much each system will contribute to the system operation under various conditions you can test using the 2WD option in the ebikes.ca simulator; it can show you simultaneous graphs for each this way, for the same riding conditions.
If the difference in system voltage, motor winding, etc., between the two systems is great enough, you could have drag on the low-speed system while at the highest range of the high speed system, with two DD hubmotors, because the lower speed motor will be acting as a generator once it's above the voltage the battery could supply to it.
While the SB Cruiser (and Crazybike2 before it) uses a common battery, it has always had dissimilar motors and controllers on each of the powered wheels (usually the two rear). So it takes some learning to control with the different traction and braking torque curves on each side, since it will pull to one side or the other differently under various conditions, speeds, and control inputs. The present setup with a Phaserunner v1 on the left side and v6 on the right, running two similar but not identical ex-A2B Ultramotors, is the most similar response that I've had out of all the various systems I've used over the years.