Sorry I was a bit dense and took ThemeForest literally.

Godaddy responds as most US companies do to DMCA Takedown Notices by removing access to the cited content. By law, they must disable access if they receive a valid takedown request. It would then be up to you to file a "Counter-Notice" with them, at which point they will enable access to your content again. The Digital Media Law Project (DMLP) has some useful info on how to file a Counter-Notice:

http://www.dmlp.org/legal-guide/responding-dmca-takedown-not...

If you contact GoDaddy first, and inform them about the false threats, they might consider any takedown request they receive as knowingly false, and not disable access to your content, and/or well as give you time time to file a Counter-Notice. It won't hurt to ask them about what you should do, since at least then you'd have a pre-existing support ticket number to refer to if they do get a takedown notice.