No. If they want you they will make you an offer - this may not be what you expected (or suggested) but you can guarantee they will have looked at the relevant salaries for the area and work and will offer you something in that region - and probably bumped up a little too.
Leave that decision on how much to offer to them. Never go back and start sounding desperate for the job by making offers to them, it never looks good.
now, if they reject you, it is reasonable to mention to your agent about the NYC salary, and that if that was the problem you would be willing to accept less in order to "join such a great team" or similar, and let the agent handle that on your behalf. Chances are though, salary expectations are never the issue for a candidate they want - if they cannot pay enough, they will come back and suggest a salary to put the ball back in your court to reject (or not).