Claiming random thought patterns probably wouldn't have worked for Dilbert, either, nor would it have revived his illusion of free will. He could also have claimed that some butterfly flapping its wings in Brazil caused the project to fail, but that would probably have gotten the same response from the boss. Trying to find the root cause of anything is a hopeless task. What the boss really wants is the proximate cause; the name of the person he can yell at or fire. The humor, for me, is that Dilbert tries to divert the boss's search for a proximate cause by giving him the ultimate cause.
Those "wave functions" are probability equations. That leaves room for a lot of non-deterministic factors. Dilbert could argue that his thought patterns are random but that argument has never worked for me! ;-)
I totally agree that quantum physics is the way to go if you're dealing with phenomena on that level, but if we turn Dilbert into a quantum physicist, it doesn't alter his situation. His answer to why the project failed might then become, "I'm a quantum physicist, so I'd have to say that the problem began with the origin of the universe, and is the result of incalculable numbers of quantum events occurring since then." If Dilbert's thought processes are the result of quantum events in his brain, he still doesn't have conscious control of collapsing all the wave functions that result in his decisions and behavior. In either case "free will" is logically incoherent.