Tradiitionally I completely agree that team and 3-position training is a bad idea. But if you are training hih skilled, low potential players (star/all-star) it could be worthwhile. Since the price for an all-star player doesn't change much when they have reach their cap rather that be at 21 or 27 you could concievably extend their training and add more players along.
But as I said, the only way it works is with trainess that have high starting skills particularly if you go the 19yo route.
All that said, it seems like too much of a headache for me and I wouldn't do it.
I haven't done much three position to comment intelligently, but fortunately that rarely stops me. ;)
I did what you're discussing with two positions instead of three and it was a great foundation to build around while working my way up the lower levels, leaving me guys who were valuable players in III and very strong Cup starters/league backups/spot starters at my current level. I did do a three position training once in an offseason week where I had three guys who were going to be receiving a lot more pressure training and two additional who were very close to their final pop. I was pretty happy then.