All things considered and with perfect hindsight, did the Allies benefit, by having Italy fight on Germany's side rather than remain neutral?
While the popular impression is that Germany had to "bail out" Italy more often than not, this does not mean they were a net burden on the Axis. On the contrary, Italy opened up the Mediterranean and African theaters of war that required an extensive diversion of resources, ships, aircraft, men, and material to fight in the very critical early years of the war. The campaign to clear the Mediterranean and then liberate Italy went on through the whole war. All that could have been instead fighting Germany.
Hostile Italians also prevented the Allies from using the Mediterranean as a "British lake" to safely supply the Pacific and the Soviet Union, as well as to stage raids and attacks on Southern Europe.
To avoid a "what if" answer that's frowned upon here, I'll instead go into the ways the Italians tied down Allied forces and delayed Allied victory.
The Regia Marina and Regia Aeronautica during WWII were a large, modern, and powerful threat, if not the best commanded, that required a diversion of large numbers of British ships, aircraft, and men to fight. This stretched the British even thinner than they already were.
Germany alone had no hope of combating the Royal Navy on the surface, but entry of Italy gave the Axis something closer to parity. The battles in the Mediterranean pulled away aircraft and anti-air artillery desperately needed for the Battle of Britain. They pulled ships away from the Battle of the Atlantic. The British Army was unable to defend Greece because they were busy fighting the Italians in North Africa and had to halt their successful offensive there to transfer troops to Greece ultimately suffering in both theaters. 100,000 British colonial troops were tied down fighting the Italians in East Africa.
It was during this critical stage of the war, 1940 to 1942, that Germany could have won. During this period the Italians were effective at tying down British resources.
The Italians also made it difficult for the British to use the Mediterranean as a British lake. It secured the German southern front against air attack and invasion. Without the Italians in the war, Britain's Mediterranean holdings could be used as a staging area for an invasion of Southern France or bombing German submarine pens in Western France.
Finishing off the Mediterranean theater required a huge invasion by both US and British forces. Operation Torch, Tunisia, and Sicily involved 500,000 troops and much of the Allied naval transport capacity fighting mostly Italians. While the Americans advocated invading France in 1943, the decision to invade Italy probably delayed the invasion of Europe by a year.
Even after the Italian Armistice, the march up the Italian peninsula remained a very costly distraction for the Allies. It's questionable what the end goal was. Germany could fight the Allies in strong defensive terrain and ultimately fall back to the defensive line of the Alps.
Without Italy in the war there would be no Mediterranean nor African nor Italian fronts to draw British resources away from Germany in the critical early years of the war, nor would there be an Italian liberation campaign to delay the invasion of Europe.
In addition to the direct effects, the Italians made the Mediterranean dangerous for use as a supply line to the Pacific and the Soviet Union.
After 1941, Allied ships wishing to reach the Pacific Theater quickly could avoid having to go around Africa by using the Suez Canal. Similarly, the Allies had a supply line to the Soviet Union, the Persian Corridor.
With Italy in the war this presented a terrible choice: run a gauntlet of Italian ships and aircraft in the Mediterranean in the hopes of getting there faster, or go all the way around Africa adding weeks to the journey and making themselves vulnerable to German U-Boats and surface raiders. Both required additional escorts. Both added risk and time to supplying these theaters.
These supply lines made it vital that the Italian navy and air force were dealt with drawing yet more forces away from fighting Germany and delaying supplies to the Pacific and Soviet Union.
ADDENDUM: Italy being in the war had a profound effect on the Pacific War. I picked up on this from Drachinifel's Drydock #43.
As above, a belligerent Italy drew away a significant portion of the British armed forces to defend their interests around the Mediterranean. This, in turn, left Britain's Pacific holdings thinly defended. Britain's plan was to essentially bluff. If attacked they would abandon their outlying holdings and fallback to Singapore, India, and Burma. Few reinforcements would be coming until the Mediterranean was under control.
The capture of the SS Automedon in Nov 1940, and her top secret documents outlining all this, gave the Japanese assurance that the British were a paper tiger. Emboldened by this information, the Japanese knew they could send the cream of their Navy on far-flung offensives without being concerned with a major British counter-offensive.
If, instead, the Italians were neutral this would have freed up significant assets to reinforce the British Far East, and allowed the British to take a more active and offensive attitude towards Japan.
ADDENDUM 2: Naval Historiographer Drachinifel and Military History Visualized did a piece on Italy's forgotten WW2 Victories? which expands on the impact of a hostile Mediterranean and the effect on the Pacific War and convoy battles.
In particular he points out...
- The fast transports and escorts used in the defense and resupply of Malta.
- The heavy units needed to counter the Italian Navy.
- The 135 British ships lost in the Mediterranean.