MS and windows activation issues aside...
If the chipsets are the same, the hardware is the same, and all things are equal with the exception of onboard devices that are able to be updated with a driver, then yes, you can "just" swap out mobos...if the chipset and devices are different, then you definitely want to re-install or things will get pretty buggy.
Back in the day, I swapped out hardware (drives, gpu, cpu, roms, etc) that came from a Soyo SY-KT333 (Via KT333 chipset) to an Asus A7V333 (also the KT333) and aside from reloading some drivers, it worked fine enough.
Conversely, a friend of mine just took the drive from his old machine and complained when windows wouldn't load properly and BSOD'd.
Again, MS activation issues aside, it can be done, but it's really not recommended.