I am running a Sapphire HD6850 off a Neo Eco 400. Its perfectly safe, but its odd that an HD 6850 needs both an 8-pin and 6-pin. The 6850 is not a power hungry card at all, it usually needs only 1 6-pin or at most 2 6-pins.
And if this is the same card: http://www.newegg.com/Product/Product.aspx?Item=N82E16814121419
it only requires 2 6-pins. And you are perfectly fine to run them both from 1 rail.