italov: I ended up on this topic after installing some mods through Mod Organizer and had some problems trying to duplicate the things discussed here. But I got a solution and I think it is worth to share with anyone who might get stucked like I did.
If anyone is having problems to make the game launches through GOG Galaxy, just use the script provided by @Demitrix2k and transform the patch with your profile on a executable exe.file. Name it the way it pleases you most (I have named mine "Fallout 3 mod"). After that, instead of replacing the original game executable with the one you have just created, you simply have to copy it to the game folder.
Now, go to the menu of the game on GOG Galaxy, click on Settings > Manage installation > Configure. Check the "Custom executables/arguments" option and click on "Add another executable / arguments". Search the executable you have created and select it. Finally, check the option "Default executable" and click "OK".
With this solution, you might be able to launch your modified game through GOG.
You no longer need to convert bat to .exe, you can link .bat files in Galaxy 2.0 my earlier guide in here was for Galaxy 1.2 which is now outdated, there are way better tools making this actually way way simpler, so il post a quick tutorial since its super easy now, few steps.
1. make a bat file with ( open notepad, paste contents, save as .bat extension)
2. paste and configure according to how you want it to launch, i do it like this
"C:\Mod Organizer 2\ModOrganizer.exe" -p "GOG-DemitriX-NV" "moshortcut://:New Vegas" (-p is for profile name you use in MO2 and moshortcut://: for the name of the executable you are using inside mo2.)
3. Go to your game in Galaxy 2.0 and click the button on the right side of play which is the options menu
select manage installation > configure
Cant find what im describing? here is a video
https://streamable.com/aomtat 4. tick and enable custom executable and click in the bottom "add another executable / arguments" and select the bat file wherever you so placed it( might aswell put it in game directory to keep it clean.)
5. select it as default by clicking "default executable" so when you click play, it will use that one instead of the default that comes with installation.
So if you've done my old method, its the steps to making a bat file, then you simply just add it as another executable and make it the default to run when you click play.
***EDIT 5/5/2024***
This method still works as of this date update, my only issue is overlay will not work properly, likely because i am running new vegas with dxvk.