Does GOG simply push updates to games sent to them by Dev's or do they need to make a request for the updates? Recently I purchased GreedFall and noticed today that it's running as version 1.0, while version 1.04 with a number of fixes and upgrades came out in October. A month and a half later and still not one update? How long does it take GOG to get updates for their games? This could be a huge deciding factor on any future purchases.

Varies from game to game, depending on how much the devs care for their GOG customers. Falling behind on updates by months or even years, or even devs downright refusing to update on GOG in a handful of cases, are an important part of why a game ends up on the "second class citizens" thread (used to also be a mix, until they removed mixes).

From what I understand, devs have the tools to upload patches to GOG, which get distributed to Galaxy, but then GOG may test them before adding the offline versions as well, or at least take some time to do so for whatever reason.

GreedFall just released here last week, so unless the devs/publisher for some reason supplied GOG with a really out-of-date version, it might be one of those cases where the version number displayed in-game is not the exact version it actually is.

No matter what GOG claimed, all their offline installers are updated manually.
Some teams do better, and some others always make silly mistakes here and there.
For example:
1. No changelog
2. Update installers but do not update the filename. That is, you download new installers but they have exactly the same filename with old installers that you already had.
3. wrong versioning scheme and wrong timestamp
4. broken patches
5. mix 32-bit and 64-bit installers in download URL
6. provide invalid 32-bit installers that never work

Where did you read '1.04'?

Steam: two patches (Oct 02, Oct 31), and one update in beta branch (public soon)

GreedFall was released on GOG last week (Dec 11). GOG's build 1.0 includes the two patches, e.g.
• "The size of subtitles can now be changed." (added with patch 1)
• "Dodge and parry are now correctly shown on the key bindings page." (patch 2)

EDIT
console patches called '1.03' and '1.04'

https://games-guides.com/greedfall-update-1-04-patch-notes-of-october-31/
It's possible that this version is the updated version and they simply didn't change the version number, but it still feels awefully buggy to be the case.

I've seen many times on that site the version numbers not matching with the ones on steam/gog, though the changelog was the same. I guess the version numbers for consoles and PC are different sometimes.

Thanks, it seems the two major updates are labeled as ’1.03’ and '1.04' for consoles (PS4 at least).
Overview: patch notes on SteamDB


I checked the Product version (GreedFall.exe ->Properties ->Details) on Steam and GOG:
• Steam's 'Patch 1' (Oct 02) is 0.01.5632.
• Steam's 'new patch' (Oct 31) and GOG's '1.0' are both 0.01.5635; game files/content are identical (cmp).
• Steam got an update on Dec 19 (no patch notes). Product version on Steam is now 0.01.5636.
UPDATE: GOG Standalone installer, and that of its DLC, updated 20 December 2019 with no changelog: 1.0 ⇒ 1.0 (5636)



Latest update is "1.0 (5686)" (Product Version: "0.01.5686"), published 30 July 2021.