If Garnett were a Laker the odds are slim that Shaq would have ever become one as well.
But I think the answer to your question is yes, KG would have rings because the Laker organization would have built around him nicely, unlike the pathetic Twolves group.
But that's not to say Kobe wouldn't have a ring or rings, because Minny would have likely traded him away and he would have won them somewhere else...