While the logic board will work, I don't think it's worth the costs and the limitations even the upgraded system has.
Todays systems really need a minimum of 8GB for simple web browsing and writing. 16GB is needed with photo/video/music work as well as running multiple windows open concurrently. In addtion 256/512GB is now the base for SSD storage.
Whats important to also understand is within the newer M series systems unified memory is more efficient so 8GB goes further. For $1000 you get a lot more and it also runs current and newer macOS's a lot longer than your 2015 based MacBook Air. As you can see here [https://support.apple.com/en-us/HT212735|How to upgrade to macOS Monterey] The 2015 MacBook Air systems are on the bottom edge. It's likely it will be dropped in the next macOS release or the followup.
I would stick with what it has and stick with the highest it can support for macOS, saving up for a newer M Series system.