They could, but there would be two things that make this impossible:
- Humans don't have the powerful tongue or strong jaw muscles like a natural grazing animal does that can eat lots of grass for long periods every day, and have to rely on their fingers and hands to pull up choice pieces of grass to eat.
- If they were to rely on it like a cow or horse does, day in day out, they would starve to death on it simply because the human digestive tract is not designed to break down such coarse plant matter efficiently enough to use it for bodily function.
There's nothing wrong with the actual activity of eatinggrass, but it's the subsisting and thriving/surviving part that would be a much bigger problem for that human. See the related questions below for more information on why.
