Over 100 posts and no mention of "Heads, shoulders, knees and toes".
As the song goes on to mention "eyes and ears and mouth and nose" the actions definitely add to the song.
The actions are also a necessity if you sing multiple verses, as on the second verse you only come in on 'shoulders', and 'knees' in the third verse. As the number of lines sung gets fewer (and the tempo often increases) it is only by following the actions that you can keep pace with where the entries are going to be.