He could go as a delegate from New York.
You are speaking of the Convention of the States option of formulating amendment proposals, not the Congressional option. That's a totally different thing.
As far as delegates to a Convention of the States, the provision of Article II Section 6 that forbids a federal officeholder from being a presidential elector would also apply to the position of delegate to such a convention. The supporters of the Convention of the States movement pretty much agree on that.
Kind of liking Vince Flynn’s Term Limits