Yes all animals like grass and need the vitamins it provides. However, the grass in the yard can cause the Yorkie to vomit is because the grass is seraded and they can't digest it.
I keep pots of rye and wheat grass in pots and cut/break it off and give to them. this prevents the problem of vomiting becaues the grass isn't going to cause a problem.
There is a site that a lady has that will give you all the information regarding plants for pets.
PLANTS FOR PETS