iOS jailbroken: native storage on an external drive?
Theoretically? Yes.
Practically? No.

You would first need to build nfs for iOS. Then, you would need to make the YouTube downloader application save its movies onto the network drive. As far as I can tell, nobody has worked on nfs for iOS, so unless you know a lot about programming for iphoneos-arm, you might just be out of luck. You wouldn't be able to extend the user partition onto the network drive, though, so none of this would be transparent to the apps. You could symlink the Documents folder for each app that you'd like to have access to your network drive, which would give you the same effect (assuming you can get your drive mounted).