Does this sound like the way the system would be laid out? motion control board followed by driver board followed by the actual linear actuator... and feedback to the motion control board via the linear encoder?
Yes.

The driver / controller sends a signal to the linear actuator to move to a specific position. The encoder provides feedback to the driver / controller to keep it up to date with the current position of the axis. The driver / controller computates the actuators velocity / acceleration and distance from the position it is supposed to move to. Using this information, the driver / controller will tell the actuator to speed up, slow down, stop, or whatever it needs to do to get to the end destination.
This is a very simplistic way of looking at it.

The driver / controller sends a signal to the linear actuator to move to a specific position.
The controller talks to the drive, The drive(power/step distributor) energizes the motor or actuator for as long as the controller is talking to it. And yes the absolute linear encoder reports back to the controller letting it know what the actuator has done. In layman's terms.

But, many other things come into play.(Kinematics, Inertia, Friction, Resistance etc..... Of course one bite at a time but in this case, you'll have to gorge yourself sometimes, as many things need to happen at the same time.

Imagine circular interpolation how complex it will be, by not following the motor or linear actuator's encoder, but by only following the absolute linear encoder. I can see problems with jitter and short step. The controller would forever seek and search for perfect position and compensate how?
If it was remotely advantageous, don't you think it would be commonly done by the "big" companies. My guess, TOO expensive to implement.