Assuming that it's possible to get the equipment (including accurate clocks) there in the first place, and that it's possible to get the data back afterwards, is it possible to do very long baseline interferometry in any useful wavelength range (radio is presumably easiest) over distances on the order of 1AU or more between the telescopes? How precisely do we need to track the telescopes' positions in space and time to be able to make it work?
A secondary question I have is whether it's feasible over interstellar scales, again assuming that you've already solved the problem of how to get the payload there in the first place. e.g. if we can insert a Kepler-like device into A. Centauri orbit, would that allow us to build a virtual telescope with a "baseline" of $~4.4ly$?
This question was originally inspired by watching Acapella Science's history of exoplanets while writing a sci-fi story involving (STL) interstellar travel and FTL comms, but I'd like to know whether there's any theorectical obstacle to doing it in standard physics, i.e. without the cheat of getting the data back to Earth nigh-instantaneously. The scenario I was envisaging involved a "fast" (i.e. $>0.95c$) spaceship - I don't know if that makes tracking the position of the telescope to the precision required infeasible for some reason.