MacBook Pro, iCloud Drive, Time Machine and Time Capsule 2

Make sure that you have a clear path to the Internet in terms of firewalls, and ensure that TCP port 5354 and UDP ports 4500 and 5353 are open and unrestricted.

Once you've done that, make sure you are logged into iCloud on your computer, and that the remote Time Capsule is on (also making sure those ports are unblocked on that end). Your disk should now show up via AFP in the Finder sidebar!

Also try these steps from the Apple Support Article about troubleshooting Back to My Mac.

• Update all your Macs to OS X Lion v10.7.3 or later (OS X Lion v10.7.4 or later is recommended).
• Choose System Preferences from the Apple () menu. Open iCloud System Preferences and check that Back to My Mac is enabled. See if any diagnostic messages are provided under the Back to My Mac section to assist you with troubleshooting and resolving any connection issue. 
• Toggle Back To My Mac off and back on by deselecting and then reselecting Back To My Mac in iCloud System Preferences. 
• Make sure the computer you are trying to connect to is not sleeping and is set to Wake on Demand. For more information about Wake on Demand, see this article.
  
• If you are using an AirPort base station, make sure your firmware is up-to-date (open AirPort Utility 6.0 or later).
• Check your network for a multiple NAT setup and reconfigure your network as needed.
• Make sure NAT-PMP or UPnP is enabled (if you are using an AirPort Extreme Gigabit Ethernet base station, click here for information about AirPort Extreme Gigabit Ethernet and NAT PMP).
• Ensure TCP port 5354 and UDP ports 4500 and 5353 are open on your firewall. To learn more about ports used by Apple products, click here.

Note: Perform these steps only if you've verified the information in the previously listed troubleshooting section is configured correctly.

1. Open Keychain Access located in /Applications/Utilities.
2. Choose the System Keychain in the Keychains list on the left.
3. Sort the Keychain list by Kind.
4. Select all keys listing the "Back to My Mac Key."
5. Delete the selected keys. You will be prompted for your machine's administrator password.
6. Quit Keychain Access.
7. Choose System Preferences from the Apple () menu. Open iCloud System Preferences.
8. Toggle Back to My Mac off and back on again by deselecting (if still selected) and selecting the checkbox.
9. Once Back to My Mac connects, quit System Preferences.

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.