Yes, you may. You’ll only be able to log into a single instance of the Battle.net account at a time, but you can have multiple WoW licenses on that Battle.net active. So you could log into WoW1 and WoW2, either on the same computer or two different ones.
Keep in mind that only the registered user of the account should be accessing it. With the exception that the registered user may allow one minor child, that they are the parent or legal guardian of, to access the account.