Sorry, accidentally did not finish that post. Anyway, he did resign from the conservative party chair and became the republican senator.
So, principle wise, yes to the conservative party, in actual practice much work would need to be done, as far as voting in primaries, in NY you can only vote in the party you are registered in.
As I said, I was a member in the late 80's and early 90's so I don't know how much has changed since then. There were many good conservatives involved but like anything, the ultimate decisions come down to the leadership.