I don't believe we would have. The dinos were already showing pack and herding behavior as well as bipedal walking which freed the upper arms to be used independently. It took us 61 million years to get to the bipedal stage, what would have happened if the saurians had another 61 million years to evolve?
Then again if you removed humans from the modern world it will be a place where sheer brawn and size will matter for apex predators just as the dinosaurs, not intelligence. Perhaps the dinosaurs would never have had developed into a tool using species and the pack behavior would have progressed no further than a modern day wolf pack.
If all mammals descended from a common ancestor then the rest of the mammals have had just as long as we have to develop into an intelligent tool using species. Yet we are alone with no competition. Did our ancestors have the right DNA at the right time in the right environment? Did aliens mess with our genes? Did a cosmic ray hit a chromosome in a fortuitous location?
I doubt we will ever know and this will remain a cerebral exercise.
To answer your question, no asteroid=our ancestors being appetizers for the dinosaurs.