Is it possible to account for motor dead-band in a Laplace model of a feedback DC motor system?
Yes and no.

If the motor will be going continually in one direction, you can sweep it under the rug by calling it a constant disturbance torque.

If the motor will be constantly running one way or another, particularly if you have an inner velocity loop, you can measure your system response (I prefer swept-sine measurements), model the system based on those measurements, and pretend that the model is accurate.  Check the Wikipedia page for "describing function".  This also works if the hunting caused by the friction is smaller than any inaccuracies you care about (see below).

If the motor needs to stop, then accurately and slowly reach a position, then probably not.  The "deadband" is from friction, and the starting friction is higher than the running friction.  This means that if the motor is on the verge of breaking loose and running, an infinitesimal increase in drive will cause a finite motion -- i.e., an infinite gain.  That's just too nonlinear to approximate.

You can do things to make a motor with friction appear to be more linear -- do a search on "dealing with the effects of friction and backlash".