Is the delay to correlate the signal from one dish to another on a VLA radio telescope longer for red shifted objects? When observing 2 objects side by side close to the horizon with a very large array, one receding fast &amp; red shifted, is the delay to correlate the signal from the closest dishes to the further ones longer for the red shifted object?
...is the delay to correlate the signal from the closest dishes to the further ones longer for the red shifted object?


Good question!

The short answer is no. The path difference between the closest and farthest dish in the array comes from local geometry, a big triangle in the air right above the VLA dishes. Here the speed of light is essentially constant (except for local temperature and humidity gradients in the air above the array, or maybe wind sheer) and so wouldn't vary between the to signals very much for reasons related to the sources' Doppler shifts. 

The interference path length difference is divided by the local speed of light (in the air) to get the time difference needed for best correlation of those two dishes, and it doesn't make any difference what the source of the signal is or the speed that it was moving.

Doppler shifted photons don't look or act any different than non-shifted photons, there's no way to tell the difference in an experiment, unless you have some information about the original frequency before the shift.

The only teeny tiny difference might be if the air has a different index of refraction at the shifted frequency than the unshifted frequency. That's certainly taken into account during normal analysis, and I don't think it rises to the level and intent of your question.