Yes and No.
NauticEd as a Yacht Charter agent also deals with the reality of this question every day. So below are the guidelines for this question.
The NO part: Yacht charter companies need to feel comfortable that you will not crash their boat - or even ding the gel coat. When you bring the boat back to the dock they have a few hours to turn the boat around for the next client. They'd prefer not to be re-fiberglassing the boat and trying to dry the epoxy with a hair dryer while the next client is loading on provisions. With that then, they require big boat experience and would prefer to see some cat experience. However if you have lots of big monohull experience then they sometimes will let you just go with a cat. Sometimes they might require 2-3 hours of a captain on board who will teach some catamaran maneuvering skills. More than likely they will advise you to call them prior to you returning so that they can come on board and bring the boat back in them selves. A smart inexperienced skipper will be very happy to turn the boat back over to the responsibility of the charter company when doing tight maneuvers. So no you do not NEED a catamaran endorsement to rent a catamaran on a sailing vacation. Experience is preferred.
The YES part: The NauticEd SLC Mediterranean license requires that you complete the online Catamaran Sailing Confidence course and log 1 day of training experience or as master experience on a catamaran of similar size, if you are to be catamaran qualified on the SLC document. (This is on top of 50 days of sailing experience, an on-the-water assessment, and the bareboat charter master bundle of courses). Part of the Yes part is that you need a sailing license to sail in the mediterranean and the SLC shows the types of boats you are qualified for. We wrote this requirement into the SLC to be educationally responsible and ensure that no charter company would come back on us.
Back to some more NO parts: The ICC and some other mediterranean licenses don't go that far as to list Catamaran qualification/endorsement. What is the overriding say-so is will the charter company themselves (as long as the legal licensing is taken care of) actually allow you to take a catamaran because of your experience (or lack of)? The last thing you want is to learn on the docks from the charter company that you don't have enough experience to take out the cat - despite being licensed.
Consider a Skipper for your first time: It is not that expensive to have a skipper for the week. AND it actually is a good idea since you will gain more confidence. The skipper will help teach you. The skipper knows all the cool places. If you want the helm the skipper will give it to you. And the skipper will keep you entertained with fun sailing stories. And the skipper might even baby sit the kids for an evening while you hit a fancy restaurant for yourselves. Here is our blog article on taking a Skipper: http://www.nauticed.org/sailing-blog/why-hire-a-skipper-for-your-sailing-vacation/
What we recommend: If you lack catamaran experience, make sure your resume reflects plenty of sailing experience and some of that experience should be on a monohull as big in length as the catamaran. Then get one day of training on a catamaran and do the NauticEd Catamaran Sailing Confidence course. This will usually qualify you.
When you work with NauticEd Sailing Vacations as the agent, will will prequalify you with the charter company so that you get no surprises on the dock.