I have read somewhere that it is possible to use feedback from a position sensor into LinuxCNC, can't remember where. It certainly is NOT possible in Mach3. However I wouldn't recommend it because putting any backlash into a servo loop make it very tricky to stabilise.
In Mach3 you can specify any amount of backlash, I would assume that LinuxCNC is similar. On my mill it is compensating for something around 0.01mm and seems to do a pretty good job. However on my lathe the Z axis lash is something like 0.3mm I think and trying to get compensation to work is hopeless. Fortunately I haven't found a job yet where I need to cut in both directions… The X axis (cross slide) does have a ballscrew.
I think there are two issues here. First, yes in principle BC will "take out" the backlash so the mill should cut to the dimensions instructed – but of course any variation on backlash over time or depending on position will reduce the accuracy. Second though, BC can't do anything to make it possible to do climb milling, so it's still possible that the cutter force may pull the work through the backlash, possibly breaking the cutter, ruining the work, and at the least affecting the accuracy. I would strongly recommend if you do convert the new mill to CNC, fit ballscrews!