I don’t think this is about grouping servers/machines in groups (for testing that, we would have enough machines, but I doubt iTunes would support it as you said), but about grouping playlists in groups.
This is something iTunes allows since 5.x I think. Folders can even be recursive, and shown over the network. Oh, and each folder shows the contents of all contained playlists.
There has been another topic here, but your question remained unanswered:
Regarding that question: yes, folders are not only shown locally, but over the network, and are recursive (otherwise I would have suggested simply adding a folder VARCHAR(64) or similar to the playlists table 😉 , but that way, we would need either a separate table for the folder structure, or a full path in the playlists table. Not sure which one would work easier in your code).