If you are talking about US, it would be a violation of Computer Fraud and Abuse Act, just like with Aaron Swartz.
I'm pretty sure, you could find a country to register your company in, where that act does not apply ;).
That seems a bit over the top 😆
@post
That would be difficult. There's nothing in criminal law that says, you cannot use an extracted API key and civil law would require you to be in breach of a contract in order to be sued.