Backing up Time Machine sparsebundles to another server
I would say, rsync away once you are sure the sparsebundles are not being actively mounted or written to by other Mac OS clients.

The beauty of an Apple disk image is that all the Mac unique things are stored internally since they are a filesystem unto themselves and don't rely on your actual storage filesystem in any way. As long as you get the file names over and the OS has permissions to re-share the files - you can't break things as you move the actual files that make up the sparse bundle directory scheme to another Linux or OS X or Windows OS.

In a nutshell, the files stored as bands in the sparse bundle format are very portable which makes the HFS internals immune to corruption when the raw data is copied faithfully to a new location or a new server with a different filesystem structure. 

In fact, having a Mac mount the filesystem encapsulated within the sparsebundle container would be a less optimal solution since it could take far longer to traverse the hard linked directory structure rather than let linux copy the file data efficiently. You would lose all the benefits of a sparse storage scheme to have OS X mount the files and copy them directly.