Technically, no. The grouping tag was originally intended to indicate that an individual track is part of a movement (you know, so-and-so's 7th symphony, 3rd movement).

Of course, there's not much use for that in pop music, and I myself have been using it as an alternate keywords field. I have a few keyboard macros that trigger applescripts that add certain keywords into the group field; I use these to build smart playlists. So if I'm listening to a track and say to myself "oh, that should have the 'downtempo' tag," I just hit cmd-cntl-opt-D.

Groupings are not designed for movements; you don't group movements, you label them individually. Groupings were designed for ad hoc groupings that are not genres. You can make groupings in any way you want: call them fun music, sonatas, blues instrumentals, whatever.

I was slightly off with "movements" but I stand by my original point. See this thread.

I thought this might clear things up a little bit. It's directly from the iTunes AS dictionary:

grouping Unicode text -- the grouping (piece) of the track. Generally used to denote movements within a classical work.

Personally, I use it for sub-genres.