Can this analog speed regulation for a DC motor be used for this scenario?
That circuit depends on indirectly measuring the back-EMF of the motor and servoing it to a constant by (again, indirectly) compensating for the motor's winding and commutator resistance.

But the motor's speed vs. back-EMF "constant" is not constant with temperature, nor is the winding resistance.

So you may get better regulation over temperature, but I don't think you'll get tremendously good regulation.

I'd recommend that you measure the speed and wrap it with a PID.  If you tune it conservatively you won't see a "jerk", although you may have to wait for it to stabilize.