If the video you post is, for whatever reason, popular enough that it could bring in ad revenue that makes it profitable vs. not continuing to host and distribute it, there is absolutely no basis for them to refuse to pay you. The reason you generally can't make money on stuff in the public domain isn't because you're not allowed to, it's because anybody can use that same thing and put in exactly as much effort as you did.
TotalBiscuit could post a public domain video, and it could make a shitload of money, because lots of people already follow him. You could post it, and your grandmother might notice. This is absolutely no different from when shows and movies that are in the public domain are rebroadcasted by cable companies. The content doesn't really have any monetary value; the distribution channel does.
If Google really wanted, for whatever reason, (I think that's a dickheaded motive, honestly) to prevent people using their services from profiting from public domain works, then what they should do is create their own public domain channel, and heavily weight it in search results for anything the collected works are relevant to. I wouldn't even be all that mad if they did; it'd make public domain material more visible and accessible to people who wish to repurpose it for transformative works.