I think it's the opposite, I think it's very likely that the Sox start Anthony next year, or he's on the roster after a month. They will trade someone if there's no injuries. Anthony will presumably be the #1 prospect next spring (Caminero who is #1 will graduate soon). He's hitting very well in AAA and it's going to be very hard to keep him down if he's mashing in ST. At the very least, if he's not starting until september 1st. Something has gone horribly wrong.
Mayer, I don't believe is going to get every opportunity to win ss/2b in spring training; a string of injuries can change a lot. He's one of the top prospects in the game as a short stop, and the Sox are not going to move him off position. Story will be given every opportunity as long as he's healthy. Mayer, who has had his own health concerns also has not taken 1 at bat above AA. They're going to want to give him a few months in AAA, but if he's performing I have a very hard time seeing him held down in AAA up to september 1st. Unless he's injured again or not performing well
Campbell might have the best chance, because he's right handed and he offers positional versatility. Now the #25 prospect in all of baseball, almost no one has the helium he does right now. He's already mashing in AAA not skipping a beat since his promotion. If he spends a WHOLE other year in the minors.......it's because something went wrong.
Teel is interesting. Because on one hand due to need he could be one of the first to come up, but he might have the biggest chance of being up after September 1st as well. He's struggled in AAA, but I'm not concerned, however it could indicate he may need a little time there before he's a finished product.
I'm also re-reading your original post, I think I misunderstood you. IDK why but I initially thought you were implying none of these guys could be up by september 1st. I suppose the probability of that is greater than 0 but I think you were saying there's a small chance ALL FOUR are called up by then.
That makes more sense, still, I can see a scenario where 2-3 are in Boston and somebody gets traded. Between trades, injuries, and players breaking down the doors, I think we see all 4 next year.