Only to the extent any damages are incurred as a result of removing or disabling access to the content, which hasn't happened. See 17 U.S.C. 512(f)(2) (emphasis mine):
(2) that material or activity was removed or disabled by mistake or misidentification,
shall be liable for any damages, including costs and attorneys’ fees, incurred by the alleged infringer, by any copyright owner or copyright owner’s authorized licensee, or by a service provider, who is injured by such misrepresentation, as the result of the service provider relying upon such misrepresentation in removing or disabling access to the material or activity claimed to be infringing, or in replacing the removed material or ceasing to disable access to it.
The countersuit wouldn't be to quantify damages from its removal (since not removed) but rather a preliminary injunction seeking declarative relief that the takedown was found invalid.
I guess you could file a claim for injunctive relief in anticipation of a suit, but that sounds like a waste of time and attorney's fees IMO. Also, you can't counterclaim unless you are a defendant, and you don't need to counterclaim to have such a claim tossed anyway. All the defendant would have to do is file a 12(b)(6) motion (failure to state a claim) in response to the original pleading.
Please read OPG v Diebold, because that's what we did and won in federal court, establishing court precedent and resulting in hundreds of thousands of dollars of fines levied against Diebold.
I did read the decision. My opinion is that the action was poorly executed, unless the point was to prematurely expend time and effort in an attempt to make case law in the absence of Diebold actually instigating a suit. IMO the would-be defendants should have waited and filed a counterclaim and 12(b)(6) motion. Case law probably would have resulted this way as well.
Also in footnote 11, the court notes that "Plaintiffs appear to have conceded at oral argument that their claims for injunctive and declaratory relief are moot and that a decision on their claims for damages will be a sufficient adjudication of their rights."
According to the decision, plaintiffs asked for and received $5,185.50 in restitution and unspecified attorney's fees, which I suppose could have been in the hundreds of thousands range if you spent too much on attorneys. The "hundred of thousands" of dollars were the result of a settlement and were not ordered by the court.
(2) that material or activity was removed or disabled by mistake or misidentification, shall be liable for any damages, including costs and attorneys’ fees, incurred by the alleged infringer, by any copyright owner or copyright owner’s authorized licensee, or by a service provider, who is injured by such misrepresentation, as the result of the service provider relying upon such misrepresentation in removing or disabling access to the material or activity claimed to be infringing, or in replacing the removed material or ceasing to disable access to it.