Short answer: Tarsnap can back up a sparse image without messing up any de-dup properties of the contents of the sparse image.
I haven't tested Tarsnap with my Time Machine backups yet, but I've used non-Mac file systems as file servers to Mac OS X clients for more than 10 years now.
The only special bit of Time Machine backups is the hard-links to directories. This requires HFS+.
A sparseimage that is an image of an HFS+ file system can use that file system to hold Time Machine backups.
Such a sparse image can be copied to a non-HFS+ file system, without affecting the Time Machine backups on the sparse image.
Using a "sparsebundle" instead of a single-file sparse image will let you use non-Mac file systems such as FAT32 that limit the file size to less than 2 GB.
I haven't tested Tarsnap with my Time Machine backups yet, but I've used non-Mac file systems as file servers to Mac OS X clients for more than 10 years now.
The only special bit of Time Machine backups is the hard-links to directories. This requires HFS+.
A sparseimage that is an image of an HFS+ file system can use that file system to hold Time Machine backups.
Such a sparse image can be copied to a non-HFS+ file system, without affecting the Time Machine backups on the sparse image.
Using a "sparsebundle" instead of a single-file sparse image will let you use non-Mac file systems such as FAT32 that limit the file size to less than 2 GB.