No... neither side really.
The ssl transfer option was created to allow users to pass cart data to an SSL server.
The technique used is that it populates a hidden form with all of your cart data and submits it to a page on the other server. That page then reads in the posted form and recreates the cart.
No SSL is actually needed on either side, it is just the most common reason to want to pass a cart from one domain to another, so that is the way the feature was named. In reality it doesn't matter whether SSL is involved or not for the process to work.