Maybe, maybe not. Sometimes the OEM will tie the installation of the OS to a particular machine. Also of importance is whether there's drivers for the new computer, a frequent issue when downgrading. If you do try it be sure first to create the factory restore discs using the program that ASUS includes for the purpose, should have been prompted during the initial setup when you got it, or you may be able to locate the program on the Start menu, don't know what ASUS uses.
An additional issue is whether you can Activate the Win7 install again, OEM licensing ties it to the machine it's first installed on.