What is the best way to compress and archive the Backups.backupdb folder without corrupting it?

I recommend using .zip. It will not corrupt the backup.

Are you aware of the aggregate size of that folder's contents, and the number of files it contains? In very broad terms, they are probably large, and millions, respectively. Compression will do little to reduce its size, considering that most larger files on a Mac (movies, pictures, music etc) are already compressed. When a TM backup drive approaches its capacity limit TM will compress backups anyway, in an effort to maximize the backup date range. That never accomplishes much either, for the same reason.

It will take a very long time (days), and you will need to move the backup off the external hard disk drive first. That will also take days. Seems like a lot of work to me providing questionable operational advantage. It would be easier, faster, simpler and probably cheaper just to purchase an additional TM backup drive and keep one of those backup devices offsite at all times.

But if you are bound and determined to do that, yes it will work.

Besides the fact that tar does not compress on its own, they don't have a native Finder interface, like zip. You would need to use the -j option, which calls bzip anyway. Two-finger tap and choose "Compress..." It doesn't get any easier than that.

By the way I don't know if tar -c -j (or -z) would work with what you propose. Zip will.

FWIW, I agree with John. Sounds like a terrible idea.