To answer your question, no. The leather/lorica/covering has no bearing on the shape of the saddle. They make a lot of versions of each design specifically for bike manufacturers with custom designed coverings in addition to their standard covering design.
They make quite a few saddles with grooves, without grooves, with and without cutouts. It's not entirely clear which model this is from your image or description as they do not have an "SL" model on their current product listing. They do have an "SLR" line and the shape appears to be of the "SLR monolink" variety which has both a non groove and groove model within it.
As stated above in the comments, it's best to go to your local shop and ask that if they do not have the item in stock, that they order one for you. Most will oblige because they can send items back if they are in unused condition. Some will ask for a deposit as a "holding" fee to ensure that you don't ask them to order a bunch of stuff and never come back.