No, it will do the opposite: It will obliterate the custom playlists on the iphone, and replace them with the default playlists from the PC. By and large, iTunes "syncs" music and related lists one way only: from the PC to the phone. (The exception is that it will copy music you bought on the phone at the iTunes store to the PC).
You could transfer the playlists on the iPhone to the PC using the free software "Sharepod". Very easy to use:
http://www.sharepod.com