Sure, why would you not be able to save a movie to a USB stick? Just make sure you compress it well enough to fit onto your stick. But since even Flash memory USB sticks can easily hold gigabytes of data these days, this shouldn't be a big deal.
The problem the other poster mentioned might be related to the data transfer performance of the USB stick or the port. Naturally, it needs to be able to keep up with the high data rates required to play back motion video in realtime. I don't see this being a problem most of the time either, but I suppose there are circumstances where date bottleneck situations could arise.