My understanding is, it’s not actually a motor command, although it’s closely related.
Consider a cortical column for a fingertip. It needs to keep track of the fingertip’s location in the object’s reference frame. That way, when it touches something, the cortical column knows what part of the object it is touching.
It’s the change in allocentric location. The same motor command will change each sensory patch’s location differently. It also depends on the object’s positioning relative to the body.
This talk could help. The ideas in it aren’t necessarily canon anymore, dunno.
Sensory-motor Integration in HTM Theory, by Jeff Hawkins - YouTube
In my opinion, we still need to define the problem of self-movement. That’s kinda what led to TBT, after all (location, location, location). It’s too easy to fill in details without realizing. “Motor output” has implicit assumptions, because it puts the execution part of motor control in a black box. Fine-tuning during movement has a lot in common with TBT: prediction error, temporal, sensorimotor, uncertainty.
To answer your question, I think yes. For example, it’d be nice to be able to say, “move this column’s sensory patch to X location on the object”. That could be wrong though, once the problem is thoroughly defined.
The cortex has axons which directly generate actions. Still, your line of thinking is close to some things in the video I linked and basal ganglia.