I don't think the main purpose of the Gish Gallop is to persuade anyone who's in doubt. It's a trick (one weird trick!) for winning debates. It depends on the fact that you can state a lousy argument more quickly than the other guy can refute it, so if you use all your time stating dozens of lousy arguments then your opponent won't have time to deal with them all.
When used in that context it may be effective in persuading doubters -- but it's not that the Gish Gallop itself does that, but that seeing the other debater apparently overwhelmed by a torrent of arguments they can't refute does it.
How "one weird trick" conquered the Internet. Some excerpt I found interesting:
I actually see this technique used in a lot of religious apologetics. There's even a name for one of them: The Gish Gallop. Would it be fair to say that this technique is taking advantage of a naive or intuitive understanding of Bayesian updates?
The "click on your age" first gambit seems a bit like Cached Selves.
Humanity's love affair with secrecy and its importance seems to go back quite a bit. The world's largest religion seems to have started out as one of many mystery religions in the Greco-Roman world at the time.