I understand what you want to do ... I'm just saying that what your proposing may not work.
Things to consider:
1) When you install a Linux distro to the SSD it IS going to add the necessary drivers for the hardware components it finds. IT does that automatically as part of initial setup. It's not something you do manually. So, when done, it will have drivers installed to the SSD.
2) The new motherboard is almost certainly going to have different hardware. When you connect the SSD, it will do a hardware scan (like it did during install) and attempt to install the needed drivers for the new components. If it finds drivers for the all, you will be good to go, but if it does not, you will have some hardware that doesn't work.
3) If, among the things that do not work is the Networking, then you're going to have a really hard time getting drivers.
So, basically, what I recommend is making a bootable USB installer of the Distro you want to use on the new motherboard. When it arrives, boot from that and run the Distro in Live mode. That will allow you to see what hardware works, and what does not. Then, you can use your still working machine to search for the drivers needed, put them on a USB stick, and have them ready when you connect the SSD to the new motherboard.
For more details, you should really visit the forum of the Distro you plan to install. They will be able to provide you more detailed help about installation and drivers.