Hylian and Delphiki are both correct:
You can infinite the other main climber if Nana has been knocked away. Even if she tries to come back and help, your f-tilts will continue to hit her as she blindly runs up to re-sync. There's a chance she'll do a random attack to swat you out, but it's pretty low.
Delphiki is also right in that you can't control Nana while she has somebody in a grab. Again, I guess there's a chance that she would repeatedly do headbutts until the opponent's Nana broke out, but I seriously doubt that would ever happen.
I really like the image of two IC's headbutting in sync. Maybe you could do it with two solo IC's on a team without friendly fire? XD