The DRO reports only the linear position of each axis. The gearing in the headstock, and hence the rotational position of the chuck, is not correlated.
In the world of CNC, rotary encoders are employed to do that, on lathes and milling machines with rotary axes.
I get it now, thanks. I overlooked that the chuck and lead screw lose their correlation if you disengage to traverse rapidly.
Your comment on rotary encoders has me wondering this: if you marked the circumference of the chuck in small enough units (say, either 100 or 360 divisions to keep it simple), then between the DRO and the marks, couldn't you hit the thread pretty accurately?