I figured I'd ask this here as I'm probably not the only one who's ever had this question, and others might want to search for the answer.

Does GOG support downloading of purchased games via FTP or SFTP?

If not, I may try out the GoG Downloader; it looks like it can queue up multiple games for download.

No. HTTP via browser or downloader. Download managers like FDM or GetRight can also be prodded to work, it's not too straight-forward though. It can, you can also try out WrathOfTheAngels' JGoGDownloader that fetches extras in addition to the games.

Why would you want an FTP download? That protocol has been broken for well over a decade. It works alright, but you're better of downloading via HTTP in most cases anyways.

HTTP is much better-suited for file transfers than FTP. The only problem with GOG's file access is the way they expire download URLs, which interferes with resuming. The GOG download manager or one of the 3rd-party downloaders like JGOGDownloader (mentioned already by Miaghstir) know how to cope with expiring URLs and are good options.

I was thinking that if each game (plus extras) were in their own folders, I could use an FTP client to highlight a series of folders, and have them download overnight. Thanks Miaghstir, I may give that a try.

Ah, that does make sense, even if the particular protocol isn't the correct one. FTP is a real PITA when it comes to NAT and firewalls.