I've always been told that the minimum length for open water should be 14'. Has to do something with the distance between waves...I'm compelled to add through my limited open water experience that length does make a difference, as does width and a myrid of other factors.
I have paddled my 14' Kestrel in open water (with a spray skirt). My husband considers me a strong paddler, yet I do have to work harder to keep up with the longer, sleeker boats. Have paddled on lakes in 20mph winds with 30mph gusts with the Kestrel. Although she has never let me down...there are several issues that will keep me from using her for a lot of open water. One of which, although she handles wonderfully in the wind and small waves, tried to ride crest to crest on the small 1 1/2 to 2 ft swells and have not been able to manage it (almost, but not quite) so I spend a lot of time going up and down (fun, but a lot more paddling).
This is one of the reasons I will have a longer boat (at least 16' to 17') before I attempt a lot of open water. There are other factors as well that I have read from previous posts that make a lot of sense and also some safety issues (like an effective roll)...but I feel yes, length makes a difference. As to over 15 ft...I do believe that would depend on the boat and/or the paddler...