The bootloader loads kernel and initial ramfs image that contains drivers. Kernel loads the rest from "normal" filesystems with the help of the drivers. Installation images do contain ramfs image that contains full set of drivers, but normal ramfs image tends to have a stripped down set, just enough to mount the necessary filesystems.
Therefore, it is theoretically possible that a new motherboard requires a driver not included in the ramfs image. In practice that is highly unlikely. Even if that happens, one can boot from Live/Install image in "rescue" mode and recreate the ramfs image with necessary drivers.
I've seen in recent Fedora/RHEL/SL/CentOS the network configuration to require some tweaking. MAC-address of NIC has been stored in the configuration "to retain consistent naming", and mismatch due to MAC having changed leads to NIC not being activated. A trivial thing to fix. On the other hand, if one does use DHCP (like most of us do) and has static rule to give this PC a specific IP, then the MAC in the rule has to be updated in the DHCP server regardless of whether the OS needs a tweak or not.
Overall, everything should be fine.