Can I install a disc-brake pannier rack on a bike with V-brakes?
Disc rack isn't an exact term. It means the rack will probably be a bit wider and make some effort to clear a disc fitted to the rear hub.
Disc model arms are brought on so the rack supports will be less likely to foul a disc :

Vs.

They both are essentially the same thing and the main thing is that new and old frame has the mounting points shown in the image:

If it lacks these then a rack will be more difficult to install. Some new bike frames will not be built to take racks. So buying a disc type rack doesn't guarantee compatibility. However it's more likely to fit.