Don't see why not. You can download a database of hashes and compare that locally. Granted, those hashes aren't "free", but that's due to the legal status of such material. The principle itself - comparing hashes - can be foss.
Yea people can look into the algorithms to see how they work and circumvent etc., but that's no different than with... Anything else. If someone is motivated enough to distribute the material, they'll make their own network. Foss doesn't make any difference here.
Don't you know, fat people can't be made fun of. It's the skinny people who are funny, see!