Yes, the Computer-Controlled Pokemon will run out of PP and use Struggle. But in Gen 1 Games which were Red, Blue, and Yellow, the Computer-Controlled Pokemon had Unlimited PP which means it can use moves without running out of PP. Look at this, it says this info in here:
http://en.m.wikipedia.org/wiki/Gameplay_of_Pok%C3%A9mon?wasRedirected=true