The short answer: Yes, but be careful.
The long answer: Obviously grass isn’t dog food and your pooch while hopefully aware of this – indulges in a little grass now and then anyway. This is perfectly normal behaviour. In fact, there’s even a word for it: “Pica is the technical term for the disorder characterised by eating things that aren’t food.” – via Pets.webmd.com
When to be worried about your dog’s grass-eating habits: VetWest suggests that dogs sometimes eat grass for medicinal purposes. In the same article they quote two studies with the following summarised learnings:
In summary, the researchers found that grass eating is a common behaviour in normal dogs, is often unrelated to illness and dogs do not regularly vomit after consuming plant material.Read the entire article here.
In a separate study preliminary findings suggest that plant eating is less common in cats than in dogs.
With these findings in hand, we ask all pet owners to be extremely careful when using pesticides, fertilisers and herbicides on or near plant material which is accessible to your pets. Also, if you are planting new plants in your backyard, please check carefully that they are non-toxic to pets.
In summary: Be careful and watchful if your dog vomits or shows any signs of distress. Consult a vet immediately.