I actually tried that and got a name of
a song, and it wasn't a takedown but an agreement to monetise (i.e. add ads, which I didn't have much of a problem), except that it was the completely
wrong song. Naturally, that song was also available to listen to in a few other YouTube videos, and the only thing that they had in common with mine was a generic-sounding section of 120bpm bass drum. The melody, the duration, everything else was different.
I disputed, explicitly pointing to the other ones which I assume was identified correctly and how they had basically nothing in common with my video, even explaining that I'd be perfectly fine with it being monetised if it was actually the right one, and was... (not) surprisingly denied. I have a feeling that either no humans were involved at all, or if one were, it did not listen or have any common sense. In the end, I just deleted the video.
Now that I think about it, perhaps reuploading with the (wrongly) detected name, letting it monetise, and show up in search results might be a better idea --- at least that will make it more likely for others to stumble across it, listen, and possibly leave comments like "this isn't X, it's Y"...