Would it be possible for Mussolini or any appropriate Italian leader to stay neutral in WWII, refusing to commit troops anywhere beyond it's own colonies and borders
Yes. Italy was neutral for the first 10 months of the war, letting Germany fight by itself.
Is this possible under Mussolini
Yes... it was his decision to hold back for those 10 months; nothing compels him to jump in.
He might have been deterred if, say, the Allies had defeated the invasion of Norway. That wouldn't prevent the fall of France, but it would dent Germany's aura of invincibility.
and what side would this be an advantage too?
Believe it or not, the Allies. IMO, anyway. Fighting Italians soaked up a lot of British resources in North Africa and East Africa. North Africa eventually became a drain on the Germans, but they caused an even bigger drain on the Allies.
Plus the Mediterranean was closed to Allied shipping. Ships had to go around Africa, tying up millions of tons of cargo space.
And while Italian troops were mediocre, they weren't useless. There was a whole army of them in the East.
The Italian navy was ultimately ineffective, but between Axis airpower, subs, mines, frogmen, torpedo boats, and what have you, the Royal Navy took more losses in the Mediterranean than any other theater.
what would the effects be?
Possible first item.
In June 1940, the British were very worried by the threat of Axis invasion. Given what surprising things the Germans had done in the previous few months, there was understandable fear of what they might do in the next few months. But it was still clear that an invasion required support and protection by naval warships, or it would be destroyed by the Royal Navy.
Germany didn't have much of a navy, and it was known that most of it was sunk or damaged in Norway. But Italy had a substantial navy, as did France. Under the terms of the French capitulation, the French navy was to sail to ports under current or potential German control, and the British feared this would lead to Germany taking over these ships.
Adding that to the Italian navy, and the rump of the German navy, the Axis could have a powerful fleet, perhaps strong enough to support an invasion. So the British tried to force the main French battle squadron at Mers-el-Kebir to surrender to them. When they refused, the British attacked them, sinking or damaging three battleships and killing thousands of French sailors.
If Italy remains neutral, the potential threat to British sea control is greatly reduced, and the British probably don't think they have to attempt the Mers-el-Kebir operation. That greatly improves relations between Britian and Free France and the French colonies; more colonies will join Free France.
It's also possible (I don't know what Hitler was thinking) that the "soft" terms given to France in 1940 (the unoccupied zone, etc) were in part because Hitler wanted those ships to help the Axis challenge the Royal Navy. If Italy is neutral, those ships wouldn't be enough. So Hitler may lean harder on France, driving colonies and perhaps the fleet into Free French allegiance.
Economically - it would be a boost for Italy, as a middleman between Axis Europe and the outside world. Britain will try to limit German imports of strategic goods through Italy, but it will be hard to stop.
Assuming Italy stays peaceful - Greece, Yugoslavia, and Bulgaria remain neutral, to their great benefit.
A possible knock-on: OTL, parts of the German army were very busy in early 1941 conquering the Balkans and Greece, and fighting the British in Libya. All this surely contributed to Stalin's conviction that Germany would not invade the USSR in 1941, and that any evidence to the contrary was a British provocation to trick the USSR into the war.
If the German army ain't doin' nuthin'; it will be a lot harder to ignore signs of its preparations for the East.
Another knock-on is that with no North Africa, East Africa, and Middle East campaigns, Britain can defend Malaya in strength. If Japan moves to war as OTL, they may not feel they can send the Striking Force against Pearl Harbor.
The war outside the Eastern Front will be the airwar between Germany and Britain, and the Battle of the Atlantic.
Mussolini will survive the war, and Italy will retain East Africa, Libya, and the Dodecanese islands, the city of Zara on the coast of Yugoslavia, and its control of Albania.
Yet another knock-on. Jews in Italy, Yugoslavia, Bulgaria, and Greece will be spared from German extermination efforts; and it will be much easier for Jews in Nazi-occupied Europe to escape to safety. For instance, OTL, Switzerland accepted a certain number of Jewish and other refugees, but soon began to refuse. Such refugees could not go any further, and Switzerland found it difficult to accommodate more than a relative few. If Italy is neutral, the path out of Europe is open, and there would be no blockage.
A knock-on related to this: OTL, with Axis forces under Rommel threatening to march into Egypt and the Axis blitz of Greece, British control of the Middle East seemed fragile, and the British government wanted to avoid provoking Arab hostility or rebellion. So the British government was reluctant to admit Jewish refugees to Palestine during the war because it inflamed Arab sentiments.
If Italy is neutral, the British don't have this worry - or it's not as serious - so Britain may drop its exclusion. This would provide a destination for Jewish refugees, and allow many more to get out in time.
Overall, the above factors could reduce the toll of the Holocaust by 1-2 million. If the whole suite happens, this could mean a Jewish majority in Palestine by the end of or soon after the war. The Zionists would then oppose partition, and the Arabs of Palestine might not dare to launch a war against the Zionists.
Later knock-ons down this chain:
Israel's Jewish population would have a much larger proportion of Ashkenazim. OTL, the majority of Israeli Jews are Mizrachim - Jews from Moslem countries in the Middle East and North Africa. Change that...
If the Arabs of Palestine don't fight, they don't get displaced. Israel starts out with about 1M Arabs and 3M Jews, instead of OTL's 150K Arabs and 2M Jews. OTL Israel now has 1.5M Arabs and 6M Jews. That suggests that by now alt-Israel would have an Arab majority!
This is wandering rather far afield - more direct effects on Italy, Greece, etc, are more important, but I don't really know enough to say how they'd play out.