Currently I boot OS X and Windows Boot Camp from an external Thunderbolt HDD. LaCie just announced a new external USB-C (USB 3.1) hard drive enclosure. Will I be able to boot OS X or Windows Boot Camp from this or any other external USB-C HDD on the new MacBook?
Considering the just announced new MacBook isn't yet generally available there are very few people, if any, that can say they've actually connected a LaCie USB-C (USB 3.0) external drive to the just announced new MacBook and booted either OS X or Windows from the external drive. That said, I'd be very shocked if one was not able to boot any OS that supports booting from an external USB device while connected to the just announced new MacBook that isn't yet generally available. Especially considering the just announced new MacBook only has only the USB-C port (and an audio jack) for any type of physical expansion capacity it would be insane that past normal functionality was not capable.
To me USB stays USB.
Type-C is just a physical form factor as Type-A and Type-B.
So yes it will work.