EDIT: Searching the web further it seems there is no way to do this. I searched the same function but instead of galaxy, for steam, which has been around longer than GOG(the bathesda version). The only answer I got is that if you wanna keep track of your playtime, run fallout on background so steam/galaxy will record playtime. I'm prolly the only one who had this question(lol!) but just thought on sharing here just in case anyone ask the same thing.

Hi Everyone!
I want to play fallout 1 using fixt for the bug fixes, but I would like to know if there is a way to run it through galaxy. I have red some topics here on this forum that discuss it in light but I could not get the step-by-step that I needed from those posts. This is prolly my ignorance here for not knowing how the mod installation goes and my noobness in regard to fallout 1 talking, but I have not found the information anywhere.

For me fixt install another folder inside my fallout folder(it's the path I chose to install fixt), and from then on fixt can only be ran from it's own .exe
Am I doing something wrong?/Not doing something?

First, click on that button with the two lines with circles next to 'Play'. Select Manage Installation, then click 'Configure' Then click on 'Features'. Check the box that says 'Custom executables / arguments'. Scroll down and select 'Add another executable / arguments'. Select the file that runs Fallout Fixt and click okay. Now click the circle 'Default executable' for the newly created lines. Click OK

Now whenever you click 'Play', it should run Fallout FIXT.