That's what I do as well. The folder that the Session file is in contains all of the Session's folders and subfolders. Pro Tools keeps a relative positioning scheme in place, not an absolute path. At least with Session files. This is how it knows where to look for your audio files, even if it goes to another drive.

You can test it for yourself to gain confidence in the "system". copy and paste that parent folder - the one mentioned with the song name and contains the actual session file and it's folders - into another directory. Then rename the original song/Session folder. Next, open the session that got moved to another directory. All of that session's data should be there and visible inside of PT.

One tiny little caveat. Until you open the Session in the new location, the Session should not open in the "Open Recent" Session list. To do this, you would have to use the Save Session As... functionality within Pro Tools. If done, it will obviously have had visibility in to the file moving activity. What I don't know is if every single file is duplicated or not. Things like any/every 3rd-party files like some plug-ins create. I've actually been meaning to test that. (Nectar, for example, lets you choose the location for some very session specific data, and I make a sub-directory within the Session's folder.)