I expect speed is calculated off generated pulses, most likely from a magnet and hall effect sensor or optical sensor, somewhere in the transmission, and the odometer distills it's count from this same source. So pulses don't care about direction, just rate.
Back in the old days, it was a mechanical linkage (e.g gears) so, depending on the design, it could actually go backwards.
I'd make sure you have plenty of space on either side of the car before the experiment... because now that you are steering the effectively rear wheels, and reversing the caster things will get unstable.
Lordy be careful, Steering in revers at high speed takes lots of skill, More than I have, that for sure. Don't want to wreck you or the Mo. Might be safest in the snow, Light amount spin-able but not grabby enough to flip you .