And specifically, did Mussolini's inability to take Greece quickly, and subsequently Hitler's invasion of Greece have any effect on the outcome of the war?
Greece was poor and war weary by the time WWII rolled along. They had just endured the "Catastrophe", the loss of Asia Minor, and had two million refugees dumped on them between 1923-26 and then endured the Great Depression. Metaxas wanted desperately to keep Greece out of the war. Greece had no navy or air force to speak of and no means to obtain them. Their army was actually quite tenacious, however. Mussolini tried to goad Greece into war. He was already at Greece's doorstep and envied Hitler's conquests. The Italians sank the Greek ship Elli on a Greek high holiday and the Greeks bit their tongues and acted like they didnt know who did it in order to avoid an escalation with the Italians, just to give an example of how far the Greeks went to avoid being drawn into the war. Mussolini finally gave an ultimatum to Metaxas demanding Greek territory to which Metaxas famously said "Ohi" (No in Greek).
The Italians had a modern military including a well armed navy and air force. In spite of this the Greeks were successful at defending their homeland to the point that they actually pushed the Italians back deep into Albania in spite of several major counter-offensives by the Italians. This was a huge embarrassment for Mussolini who had not conferred with Hitler before invading Greece and who now had to ask for his help in defeating them. There is some debate as to whether Hitler would have eventually invaded Greece anyway in order to secure it from the Allies but he probably would not have done so before Operation Barbarossa.
The Greek mainland was defeated in three months by the Germans and Crete in six months. However, the invasion of Russia was delayed by that six months and that's probably the most significant result of Greece's involvement in the war as the delay may have been the difference between the Russians eventually winning versus the Nazis.
In addition, the Greeks' victories over an Axis power were the first significant victories of the war and were cited by Winston Churchill when he said "Hence, we will not say that Greeks fight like heroes, but that heroes fight like Greeks", during the dark days of the war.