My name is Patrick Forrester
I am the maker of sails for Falcon Sails LLC.

I have been sailing most of my life.
5 years ago when somebody would ask me about kayak sailing I would say the same things most people with a little sailing knowledge would say.
In the past I said you need a centerboard, or lee board, or keel to properly sail.
Though these bulky appendages can help on some points of sail, they are required for no points of sail. For kayak sailing and kayaking in general they are undesirable.

We have just started our website, and I wrote in some detail about what direction can I sail in that you can read about at
http://www.falconsails.com/KayakSailingFAQ.php#direction
The short answer is if everything is optimized you can paddle sail within 30 degrees of straight up wind and get useful propulsion.
With a good sail on a windy day you can sail upwind beyond reaching very easily with no paddling.
In any case it is not a cut and dry answer.

I also wrote about the need ( really lack of need / undesirable nature of ) lateral resistance appendages ( centerboards, lee boards, dagger boards, keels ) at this web page.
http://www.falconsails.com/KayakSailingFAQ.php#centerboard

Even though I thought it was a bad idea initially, the first time I paddle sailed in the wind, I was hooked.

Now I rarely hit the water without carrying a sail. It does not get in the way or slow me down. A full kit weighs less than 4 pounds and folds down to about the length of your forearm.

If you have any questions you can contact me by way of our website.