Linux: no, but not necessarily plug-and-play. My daily-driver install is literally pre-configured on a VM and cloned to all of my machines with various motherboards. Nvidia complications aside, a default Linux install will contain nearly every driver you could ever need to get up and running. However, some motherboards do need you to chroot from a live environment and make it "aware" of the existing GRUB bootloader.
Windows: At best, you'll need to reactivate. More often, it'll be missing a driver or just not work as well as it did on the old motherboard. It's better to reinstall Windows.
Will admit that I'm very biased against reinstalling Linux anew except as a last resort since it's a painstaking days-long process to configure things just right for my picky tastes.