Assuming the Sox would have made the post-season is a big leap, but they were absolutely headed that way. The biggest issue I had was the unprecedented run the Sox were having with an extremely high percentage of high profile prospects who simply didn't flop. Cherington was certainly far too stingy to deal any of them, but at some point it would have made sense.
However, while pretty much every high profile prospect for the Sox to suit up in recent years has panned out, some of them, notably Bradley, did take a while. So the Sox might have had some mediocre seasons while waiting on a few others.
Now the plus there is with Cherington, the Sox wouldn't have made the foolish Kimbrel and Pomeranz trades (anyone catch Margot the other night?). But he almost definitely would not have acquired Sale, either, which was move that did make sense. And for that matter, I'm not convinced going after Price was his style, as he tended to use free agency the way Bill James recommended and S5 pointed out, which is a method that I agree with. But it can also have some short term implications.