You can uninstall all the old drivers before you remove the HD from the old mobo.
And it will work, but the odds are against you getting it done right and it working to its full potential.
Its best to back up everything, My Documents, profiles for controlers, Teamspeak etc. and reloading the drive with a fresh install. Once its all set up I do a Clone and burn it to disc, so I can reload it if need be in less than a 1/2 hour.
I personally buy a new drive for the new system and slave in the old drive, so I only have to move the files I want once. Then I format the old drive and set it up a slave drive, and copy the New sytem to it and make it dual boot and redirect MY Documents, My Games, etc to it's extra space So the next time I don't have to move anything that I can keep out of windows. Plus if my OS or if the new drive fails, I still have access to my machine.
After all these years I have several old drives I've put into external drive boxes and keep stuff backed up to them if its something I don't need all the time.