it really all depends. Sometimes it works, sometimes it doesn't. I would strongly suggest if/when you have to do this to be sure to have written down your OS' verification code (or have the discs) just in case. The other thing that can usually help a lot is to use the same brand of motherboard, and brand of chipsets... i.e. if your old one was an asus, get a new asus... gigabyte, etc etc etc.
If you're just doing a repair type replacement with the same exact type of mobo, you really shouldn't have much of an issue unless the bios isn't the same, or even close.
Taking a harddrive out of an amd computer and putting it in an intel mobo/cpu or vice versa usually requires a completely new install. The OS won't recognize the chipset signatures and will require a new install... that's when you must have the code.
sometimes you can find your personal saved info after doing a repair, but things won't run right and you'll have to reinstall the OS and anything like games... adobe, big programs. A lot of the time you can still get the adobe files, certain character game info (data only) files, pictures... things of that nature... then doing a reinstall of what's needed.
Best of luck to both of you!