But Tarkin was still trying to find the Rebel Base, so he would still have destroyed Alderaan...
The Rebel base wouldn't have been discovered though, as Leia would have been killed as you said. The Empire would have gone mad with power, destroying all planets suspected of harboring or aiding the rebellion. As the Bothan spies are under the Emperor's watchful eyes, the rebellion wouldn't have gotten accurate plans for the station.
The Death Star would have been destroyed eventually however, as it would only be a matter of time until a high ranking Imperial Death Star technician would have his planet destroyed, leaving him with an axe to grind and a battle station to grind it on.