Yes, it does, and very nicely too. With each file type found listed as a different color icon, clearly showing how many files of each type. Now that I am in the actual process of recovering those files, I will revise my answer to say, that after doing a FULL scan of the erased drive (which only seems to come up once you do a partial scan), Disk Drive shows 851GB of recoverable files, on the 1TB drive. (Not 1.5TB, as initially reported). They are both user and system files - the whole shebang.
It looks like it will take about 6 hours to recover the files (and about the same amount of time to scan the hard disk drive). Moreover, I am really happy to see that my file structure appears to be intact! It is recreating not just the folder structure, but the original file names. And I have already checked some large (~400mb) video files it recovered, and they do work.
Of course, I had to recover the files to a different drive, as Disk Drill wouldn't allow me to recover them to the original drive (just said it didn't have enough space?!). It even found and allowed me to recover the lost HFS+ partition, of the erased drive. Not sure I can do anything with that, because I very much doubt the Apple system will allow me to just copy all the files back to the original drive, and then allow me to boot it, like it was!
But that's okay. The data files are what counts. Once I copy them back to the original drive, I will just reinstall the High Sierra OS. It wasn't being used as a boot drive, anyway, so it doesn't strictly need an operating system.
So yeah, I got real lucky this time... I don't know if DD can also recover a formatted drive... But if there's even a possibility "Data Rescue" can, that's very nice to know.