|MadSci Network: Evolution|
Grass is indeed very important. Perhaps the most important thing about grasses is that, unlike many other plants, the leaves grow from the base, not the tip. That means that even if the tip of the plant gets eaten, the plant will continue to grow. Provided it is not overgrazed, it is very sustainable.
There is an absolutely fascinating book about the importance of grass that you might find interesting. It is called The Forgiveness of Nature, by Graham Harvey. I couldn't find it on Amazon, but here is a list of other possible sources.
As for your actual question, I'm going to wimp out. I just don't know, and I don't think anybody does. No grass might mean no savannahs. And early humans certainly exploited the savannahs. But if not grasses, maybe something else. Sorry, but I don't really think the question can be answered. It's a good question though, and one that could probably be discussed all day and all night, so thanks.
Try the links in the MadSci Library for more information on Evolution.