Depends on how savvy the perp was. It would have taken a warrant or court order to get Tumblr to give up the IP address, and if it came from overseas or through a proxy, good luck tracking down the perp. It can be done, but it depends on how many resources the authorities want to dedicate to it.
Agreed, they would be the last groups I'd call in on a neglect or cruelty investigation. Local AC would have been fine but without a location that's a nonstarter.And calling PETA or HSUS and giving them free ammunition is just plain stupid.