Yes, nonpartisan elections would probably be bad for the Republican Party in New York. But that's hardly a reason for LBOers to support it, since the research showing that nonpartisan elections lead to lower turnout (especially among low-income voters) and a greater role for campaign spending and name recognition bears no such caveats.
There's a nice article on this, "Teams Without Uniforms," available here: http://www.themayorslatestbadidea.com/main_analysis.htm (scroll down for a link to the full text.)
Josh