How do you think we arrive at the strong path in the first place? By trying a bunch of suboptimal paths and going "gee, that strong one I tried shaves fifty turns off my victory time no matter what else I do, it must be the best one".
Actually, as far as I can tell, the preferred method is finding the first strong path that works and then failing to see if anything works better.
As another example, several years ago, every top player of Civ 4 would tell you that Engineering was crap. Whenever you asked one of them some questions to determine whether they had actually
tried early Engineering, they would never answer.
They
could never answer.
It wasn't until a few years ago that someone started seriously experimenting with what Engineering could do, and the Engineering bulb was born.
The same attitude of "whatever works first" was also displayed in the sheer number of people would who only play until they bulb Liberalism, even when someone demonstrated that an earlier Liberalism bulb leads to a later actual victory time.
There's also some self-reinforcing nature in the whole thing; the person who learns how powerful an axe rush is when conditions are right starts setting up the map so conditions will more often be right (witness the first ALC Saladin game, where things got flubbed when early war was not easily feasible).
That this can apply in BE is rather obvious, since I recently had an argument where the entire point of contention ended up being that I tend to play on maps where I don't have two safe available surplus trade routes in the early game, while other people apparently always have them.
To sum up: no. Just based on the forum experience of the past several years, most people
don't actually continue experimenting after they find the first way that works. Instead, they raise the difficulty level and set about finding better ways to make what worked work.