I'm not sure they've really employed the strategy you are suggesting. They definitely seem to like the idea of grabbing someone with 1st round grades with pick number 2 at a premium price (See Bonemer), but it wasn't at the expense of not taking the BPA with the first pick. Hagen Smith wasn't second tier. He was even paid over-slot by $300K. The money for Bonemer and others came from "punting" later picks. See picks 10, 9, 7, 6.
We talk about it a lot during draft time but I don't think we've seen the White Sox truly reach and get a player that isn't arguably the BPA with pick #1 with the goal of it being a large savings to spread to later picks. At least not in recent years. Jacob Gonzales was under-slot, but he wasn't a reach. Just uninspiring.
I think it would be pretty fascinating if they did get a substantial savings with pick 1 and see how that plays out. I imagine Kayson Cunningham would take a pretty big haircut. Steele Hall maybe saves you 500K since he probably has a landing spot with the Rangers?
I'm really into the up the middle prep SS guys currently, but I still have this feeling it's going to be BPA college pitcher at 1 at little to no savings, then prep position player that needs to be over-slotted with pick #2, and punting some of the 6 through 10 picks again. Pretty much a duplicate of what they did with the 2024 class.