If the corruption is based on a value, different for each client (eg, a random number or the serial number of your motherboard), how do you reverse it ?
If you can't reverse it you can't seed it anymore and BitTorrent breaks
Even if that's not the case they'd just switch from grabbing a hash of the entire file to finding sub-hashes of the file or other fingerprints. You'd have to do a lot of corrupting to make this worth it.
If adobe premiere can sync my audio tracks when one is barely audible and the other has background noise you better believe there's a service that can find stored movies against a database of files
Also if you're already using BitTorrent why are you sharing these files on Dropbox et al
The idea is to save the file on Dropbox, but wrapped in symmetrical encryption so that they don't know what it is. You know your key because you created it, but they don't.
Your torrent client would see the normal file, they wouldn't see anything except random garbage.
Why? Um, perhaps to have a "torrent box" which stored data in a more accessible place?
Perhaps just to crap on someone's stupid censorship.