The Germans had no intention of invading Greece or getting there through Yugo...
But the bloviating idiot Mussolini (watch me swing from my toes, Hitler!) tried to invade Greece and fucked it up so Bad that the Germans had to clean up the mess. Sort of like they fucked up Ethiopia. And Libya. And became a millstone around the Austrian Painter's neck for the whole war. Sort of the Fiat of invading armies.
This Italian adventure diverted quite a few German divisions from the planned USSR invasion... and delayed Barbarossa significantly. This delay cost the Germans Moscow. Not the war. But Moscow.
Loss of Moscow would not likely have caused USSR to "Surrender" as they would have still moved everything East into the Urals. including the Politburo. Which they did anyway... all the factories and economy. So nothing would have really changed, except Moscow would have been destroyed. But the Wehrmacht would have taken Moscow almost certainly if they had another month of weather. Which would have had a psychological impact on the war... If not an ultimate outcome change.
Read Richard Overy... Why the Allies Won. From the '70s. An economists analysis of WW2. And he showed beyond reasonable doubt that the Krauts, Wops and Nips were finished before it started. It all came down to economics. And the Axis were too stupid to do the math. You know... racial supremacy and all that. Including the Dagos... who thought they were Roman Legions or something. When, really, they had spent 1800 years drinking water out of lead pipes and fought accordingly.
The Best of Italy migrated to New York in the early 1900's... Just 'sayin!
Cheers,
Sirhr