Can I copy those .sparsebundle files to an external hard disk and expect them to work as Time Machine backup resources again?
Almost certainly yes.
Modes and ownership
Ideally, use chmod(1) and chown(8) to have the mode and ownership, of the copy of the disk image, consistent with how Mountain Lion normally creates a local disk image for Time Machine.
Example
GPES3E-gjp4-1:~ gjp22$ sudo ls -al /Volumes/tall/com.apple.backupd/GPES3E-gjp4-1.sparsebundle/
Password:
total 16672
drwx------@ 3 root staff 10 7 Jun 19:07 .
drwxr-xr-x 8 gjp22 staff 10 6 Jun 18:57 ..
-rw-r--r-- 1 root staff 500 7 Jun 18:03 Info.bckup
-rw-r--r-- 1 root staff 500 7 Jun 18:03 Info.plist
drwx------ 2 root staff 78855 7 Jun 19:07 bands
-rw-r--r-- 1 root staff 444 7 Jun 18:02 com.apple.TimeMachine.MachineID.bckup
-rw-r--r-- 1 root staff 444 7 Jun 18:02 com.apple.TimeMachine.MachineID.plist
-rw-r--r-- 1 root staff 1473 6 Jun 21:28 com.apple.TimeMachine.Results.plist
-rw-r--r-- 1 root staff 10698 6 Jun 22:24 com.apple.TimeMachine.SnapshotHistory.plist
-rwx------ 1 root staff 0 19 Mar 19:36 token
– and for each band, you should have:
-rw------- 1 root staff
Attaching the copy of the disk image
With Terminal, for the example above:
sudo hdiutil attach -readonly /Volumes/tall/com.apple.backupd/GPES3E-gjp4-1.sparsebundle/
If you use Terminal from within Recovery OS: you'll probably not need the sudo prefix to the command.
Additional detail
… whether I can still restore …
You require:
- a copy of a Time Machine destination, a copy that will be good for restoration
- not an additional Time Machine destination.
Assumption
You wish the copy to be usable, for restoration only, in the event of loss or failure of the Time Capsule.
If the disk is attached from a local image where modes and ownership vary from the norm for a local image:
- OS X or Recovery OS might use that disk without difficulty; I can't be certain.
Thoughts
If you're preparing for the possibility of loss or failure of a Time Capsule – and restoration from a copy of what was there – then think a step further, to backing up without the original Time Capsule. (If you wish the copy to be writeable by Time Machine, that could be a separate question.)
All things considered
It's probably quicker and simpler to use the external hard disk, or a part, as a Time Machine destination.
Best Answer
As the comments say you migrating time machine backup to exFAT is a relatively long thing to do. However, if you want to just access the files from a exFAT formatted drive you can simply copy those files to that drive. Though this is not a great solution.
If it's possible try other options. Do not limit yourself to use exFAT.