Hmmm, yes and no.
Yes, it's your Library and you can do anything you want, and it will copy to the Exfat disk - though you may have -36 errors along the way.
If it all goes well then should you have to restore from there you might be able to copy it back without -36 errors along the way, and it might work when you have done so.
No, you shouldn't. There's a good chance that the library will be damaged, as it's meant to only sit on a disk formatted Mac OS X Extended (Journaled). If you then update this back up at any point, as you surely will, the likelihood of damage increases greatly.
The lest expensive solution to backing up is a USB or Firewire drive, with a wired connection, formatted as above.