It does strike me as a little odd, as satyrs are typically much more inclined to pure sex than romance. But hey, why not have one who's asexual, or just less sexual than his/her peers?
You have a unique elven group, the culture you made up, so the same should be said about the satyr.
The stereotypical (mythical)satyr is overly sexual, but like humans, I bet the average satyr is not the stereotype.
Nothing in your world has to be what is already made up in our world.
The satyr could be just a goat legged human, with all the failings a human can have.
I agree with Severin -- and you can always take aspects of the traditional "satry" but also meld in some of your own. In my story the Satyrs were once a proud and powerful race, but they destroyed themselves through their own hubris. In this case I kept some of the negative qualities, but I did not make them an overtly sexual race since they treated relationships just as humans would.