Not As far as light could possibly perpetrate
On earth, we can receive signals as far as the observable universe according to current physics could allow, eg CMB. This being in turn solely depends on how sensitive the equipment you have access to is. As atmospheric scattering is one of the things which throw off data of earth-based astronomy, you do have a definite limit for a radar pulse of individual frequency and amplitude, but by just,MORE POWER(If you don't mind vaporizing the immediate atmosphere) that could be overcome. Meaning that really, the limit to you're radar is really just the output of your generation and the sensitivity of your receiver, which would put them at odds and create some interesting dynamics.
If you had radar power stations, power by something along the line of nuclear reactors you could probably use even just use optical radar to map the surface of you're flat earth down to the buildings present like orbital satellites do on earth. This does mean airborne radar is valuable, if only for mapping. You probably could also track large groups of humans moving with that method as well. You would have to do it in segments as optical radar can' track moving objects, but still, and that's moving objects with high accuracy, they'd probably just be something along the line of shapeless blobs, Or, In short, once you remove the curvature there is no real limit. And so, yeah.