I think it's up to interpretation. Irene Adler only writes this in her letter to Sherlock Holmes: "As to the photograph, your client may rest in peace. I love and am loved by a better man than he. The King may do what he will without hindrance from one whom he has cruelly wronged."

So the king may have lied, or Adler could have sent the threat and then changed her mind. Or perhaps she was never going to go through with it in the first place.

I have a feeling that if the king had lied, Holmes would have deduced as much. I also have a feeling that the King of Bohemia had to be a major douchebag, since Adler seems very reasonable otherwise.