Nope.* Neither does rarity, or which exact dragons you combine. What I feel does sometimes influence the outcome is which combination of colors you use. Like, if you want to breed Pinata, for example, and you combine red/yellow and green, you get different fails than when you combine green/yellow and red, or red/green and yellow. I can't tell which combo is more prone to give you Pinata, but the two-color fails are biased, somehow.
one exeption: the Prime dragons. For these you need to have both parents at lvl 15.