Just wanted to throw this out there . . . in Montessori, kids are diagramming sentences with 3D manipulatives as they are learning to read, and they learn the parts of speech through activities and short explanations waaay before independent reading. So for instance, the teacher will define an adverb and then say, "Janey, tip-toe QUIETLY", "Tommy, run across the room QUICKLY" etc. There are some really great M Language presentations (free online MOTEACO and more) dealing with introducing grammar that are definitely worth checking out if you are interested in teaching grammar to a pre-reader or very young child.
I don't think it's necessary to learn grammar very early, but I don't think it hurts either.