The processing that goes into the phosphor and waterfall displays is usually overlapped FFTs, which is also the processing for a lot of common channelization techniques. So yes, probably not so much in the commercial space, but certainly very useful. In fact I'm aware of platforms that don't even store/manipulate I/Q data, but the overlapped FFT data since it's usually much more useful as a starting point.

Oh, yes it is. It is a necessary step for all radar processing in FMCW systems.