A motherboard RMA will be for the exact same motherboard as a rule.
It might have a newer revision level.
Your old OS (windows 7 perhaps)should boot with the new motherboard, and at most, you might need to update chipset drivers.
If ASUS no longer had the same motherboard, but had to send you a different one, you will probably still be able to boot since the cpu and supported chipset will be compatible.
If your os is OEM, then, yes, it is tied to the old motherboard.
At activation time Microsoft will detect this, and you will have to call Microsoft to get it activated. You will need to explain that a exact replacement is no longer available, and that your copy of windows is installed nowhere else.
And... as USAFret suggested, protect your valued files just in case.