Tilling it up will only improve the growth. The no-till blends are usualy hardy seed types that can compete in a less than ideal environment. Give them the best chance to succeed and they'll perform better than billed...
BM was right in his advice. Its almost a given you have to go two rounds with weed killer. When the weeds seem to be recovering, hit them again and you should be good. The most important thing with no-till is making sure to get decent seed to soil contact, which I'm sure you know. That's why removing the excessive dead vegetation and running a disc, tiller, or even harrow drag over the area is a good idea. The better the seed bed, the better the growth. Even from seeds that are billed to grow with no tilling. The best looking plot I have ever had was a no-till that I turned with a disc...