Highly doubtful. No 'net connection while filming, right? Even if they could (in some manner) latch onto anything you were downloading, this would be such an enormous mess of data that it would be virtually unusable.
See, here's the thing. Databases can only read squiggles. That is, letters, numbers and some special characters (others are, like >, reserved for operations). That's it. They can't - yet - read images. So without any metadata about these images, or only minimal metadata, there's no context for spy agencies or anyone else. Your videos, when downloaded onto your computer, are named, by default, with a date stamp and not much else. How can an agency, which would be (by definition) culling through thousands if not millions of pieces of data every single day, be able to sort the wheat from the chaff? Images of your grandchildren are lovely, but they are hardly what the NSA or any other agency is looking for. Your videos, like I said, are downloaded from recorder to PC with incredibly generic names. What's the difference between your Image01-05082014
and my Image01-05082014
Manually checking every video would take so much manpower that nothing else could ever be done. Checking it by computer is close to impossible without metadata. And hiring all those people would be noticeable, and using all that computing power would put an enormous strain on the grid.
If your neighbor decided to do this, he or she would have to be mighty skilled, and have some rather sophisticated equipment. If Joe Neighbor is doing this, then he's doing it to a bunch of other people, in order to justify the expense and hardship of buying or cobbling together such a system (which I still don't think is a possible system under the current state of our technology, anyway). Someone leeching all that power is going to be noticed by the authorities.