how long does it take after a developer has uploaded a patch to GOG does it usually take to show up?

Generally a day or so. Depends on a number of factors and since GOG tests patches in-house before releasing them, it can take longer. Is there one in particular you're waiting for?

It varies.
Unlike Steam, they do some tests before letting you download a new version.
There's no other way for them to make sure the game is still compatible with 'X' OS, for example.
It's a good thing, you can't always trust the word of the developer of a game.

Couple of hours to several days. If they get the update in the weekend, it's almost guaranteed they won't release it before monday.

There's no real solid answer to this other than "it depends". It could take hours or it could take weeks, depending on how much work GOG needs to do in order to test the quality of the results and prep the game builds for standard download and Galaxy, and depending on how many such games they need to do this with and what other work their employees have on their plate at the time. It's even possible that they encounter problems and need to contact the developer back and forth to get them resolved first.

So, it could be hours or weeks, but I suspect it is usually within a day or few days on average and the ones that take longer are probably special cases. If I remember correctly though, they're also working on infrastructure to potentially allow game developers to push their own updates in the future more quickly however I believe that remains to be seen yet and has its own pros and cons.

thanks for the help everyone:)