If you're willing to do a bit of assembly - yes - sort of. There are some very small cameras used by r/c modelers and others that can be hacked with weatherproof housings and external battery packs. I'd imagine with a large enough USB cellphone external battery you could get the life you are looking for.
As for the quality of the camera - in particular license plate details - please do some research as it has been awhile since I've looked at them. One brand that seems to have a lot of online support is Mobius but I'm sure there are others.