kind of interesting question.
it has been my experience (to the best of my recollection) that after a week's worth of games (that first week) my player's GS rose / adjusted. So what would training GS accomplish that week? Double the rise (from respectable to proficient in one week) or would it be redundant (respectable to strong no matter what)?
if i had to guess, it would be redundant. i think the GE is geared to increasing / maintaining GS through playing time, and that using training time on GS is a waste (with exceptions that should be infrequent -- injuries, the occasional overtime game that puts a player above 85 minutes, that sort of thing).
now let us hear from someone who knows what they are doing.