In my opinion, once the tile is placed on the green board or backer board, the mastic needs a good 1 to 2 days to dry out and cure. If you grout too soon, you will seal the area up and allow drying to alter.
Now, to answer your question, grouting is such an easy and fast job that I would think you would want to do it and be done with it. If you have the proper tools, the rubber squeggie, and pre made grout, just do it.
I have never did sections at a time when grouting, so I really do not know any advantages or disadvantages of this section type grouting program.