Sadly too, thinking that a better and faster processor could have made any of the Apple II variants into a contender that could compete and outclass emerging technologies from other manufacturers is rather like thinking if you simply put a bigger engine in a Trabant, you could compete with Ferraris at Le Mans.
Of course when you're talking about the Apple IIgs you can't overlook the fact that the original II architecture was so tightly integrated and non-extensible that backwards compatibility had to be implemented essentially by building the whole Trabant into your new racecar; they share the same engine but to run older software you have to throw a lever that lifts the racing slicks off the ground so the original 13" donut wheels can cart you slowly around town through a copy of the original transmission. (Wacky column shifter and all, and of course the engine is rev limited in this mode so you don't immediately turn all your gears into sawdust.)
I've never used a IIgs with an accelerator, I guess, but I think it is worth reiterating that at the 2.8mhz the IIgs actually shipped at its performance seems very much in-line with the 8mhz-ish Turbo XT clones that were becoming very cheap entry level options by 1986. The IIgs has a nicer sound chip, but most of the "best" games for a IIgs were also available in versions that ran just fine on a Tandy 1000 which could be had significantly cheaper, especially if you were wanting a hard disk with that. (And they were probably available on the Tandy 1000 first, because so many more of them were sold.) Even if we argue that an 8mhz IIgs is more comparable to a 286 class machine (which is debatable, especially if you don't overlook some of the severe bandwidth limitations embedded in the IIgs architecture, well, keep in mind that Compaq introduced the first 80386-based PC the same month the IIgs came out. The whole point of the Macintosh II was to compete with that. The IIgs is completely out of that league.