Is it reasonable to run the defrag and the backup at the same time overnight (i.e. would they sort things out between them?) or am I risking the reliability of the backup?
Defragging moves stuff around the platters, so all you're likely to do is make your backups grind to a halt as it plays a game of cat and mouse with the defrag software.
Most defrag software will run at the lowest priority anyway and not do much if other stuff is using the disk.
You mentioned the defrag takes four hours, how long does the backup take ? You could perhaps contemplate a fancy script that runs a defrag, checks for completion and runs a backup.