LinuxCNC can do up to 9 axis, so yes you can do a single axis CNC (which is what an ELS is). I did that on my Boley, for which I had no change gears. I just made up a bracket to mount a motor and pulleys to drive the lead screw, kludged up an encoder, and PSU, and used a PC to control it. Was never a permanent solution, I only used it to cut the nose spindle thread in a backing plate.
Backlash is less of an issue for a lathe than a mill, as you mostly don't change direction with the tool in the part (at least not on both axis), and you don't have the issue of climb milling. My mini lathe has pretty bad backlash on both axis, but can still turn somewhat precise parts open loop using LinuxCNC's backlash compensation. I suspect that closed loop with linear encoders, with significant backlash in the screws, would be pretty tricky to tune the PID loops on.
However, as Cornholio said, it is best to simply engineer out the backlash. The Schaublin has no linear encoders, so I am DROing off the motor encoders. I would not buy a ballscrew kit with cheap rolled screws. Get some nice C3 or better ground ballscrews pulled from a fab in Korea, and make up you own mounts.
One of the big advantages of CNC is that you can put on enclosure, or at least better shielding around the chuck and constrain the mess.
You mentioned using an ELS to cut to a shoulder. Nicer is using two axis CNC, to cut to the shoulder, then retract out before it starts rubbing and chattering, and returning for multiple passes
However I also really like manual lathes for quick bodge jobs which need no precision, and like the "feel" of machining on a manual lathe.
As Cornholio has said, if you are going to end up with a full CNC, you are probably better off doing it all in one go. Doing a mixed CNC/manual interface is harder to do well, than one or the other.
With the Schaublin, I found my initial use of the machine, with a loose wireless keyboard, and touch monitor leaning aginst the tailstock, to be pretty sketchy and unsafe. I felt a lot more comfortable with the safety once I built the control module with some physical buttons like feed hold, the encoder for feedoverride, and the jogging joystick etc.
The 7i73 is so cheap, having a single Cat 5 cable to you human interface can saves hour of discrete wiring.
I choose that set of diverse cards on the Schaublin for two reasons:
1/ when I went through and made a list of all the I/O, encoders, etc it would need, it was not going to work on one of the integrated cards. I currently have six encoders, (Spindle, X motor, Z motor, feed override, spindle override, jog override), with two more planned ( X Jog wheel, and Z jog wheel on a manual jog pendant). I also need a second 7i84, instead of the sketchy relay board to use available 7i84 5V outputs to switch 24V loads.
2/ I knew I would have a space challenge, and breaking up the cards reduced the need for a single big footprint in the control cabinet.
On the mini lathe, I just used a 7i96, and on the Maho a 5i25/7i77 (The 7i97 didn't exist yet), plus a 7i84 as it needed addition I/O.
Cheers,
Mark