Not really. Game Theory (in this iteration at least) is about identifying equilibria, not about the process of reaching them. This is one of several "deviations" of Game Theory from "reality". The fact that equilibria are fixed-points and can be explained in some sort of bargaining process doesn't really mean that's how we should actually imagine them. If we do so, we both overstate the theory (claiming some sort of actual behavioral process) and understate it being a (possibly quite general) fixed point to many possible market and non-market processes.

If you want to make Game Theory collide with reality, the actual convergence to an equilibrium is only one of many venues where there is a large divide. Other assumptions of these models - from rational behavior to uniform prior assumptions - are equally problematic.

Game Theory models are nevertheless very helpful because they require you to actually lay out your assumptions or - when you observe something else - reason about "what else is going on" in any of these areas. As it turns out (as another person has said), it is also immensely helpful when designing mechanism (i.e. games) like a Steam store or an ad auction, which is why tech companies hire quite a few Game Theorists.