Filing a false DMCA claim is perjury. However, not a single person has ever been prosecuted for this.

Criminal offense in that it's perjury, but you could also be required to pay the other side's legal fees.

As far as I know, punishment for the perjury has never happened. The only case I know of where legal fees were paid is Automattic vs Steiner.

Judging by all the other spam I get I think no. Especially if it's just a notice that they have no intention of actually following up on.