First of all the decision to enter WWII was taken by the leadership of the Fascist Party, not directly by Mussolini [it seems he wasn't that sure]. His driver, Boratto, in his diary wrote that an officer of the Air Force [Italian Air Force] told him that they moved the same planes from a military airport to an other in occasion of a visit of the "Duce" [just to make him happy because he thought that Italy had a lot of military planes!].
Historians tend to think that this was limited to high tech planes, for the rest the planes weren't always the same. Anyway ... if we think to the curious conception of armored vehicles that they had in Italy ...
Like any Party, the Fascist Party thought to the perspective of its political future. Germany seemed to be able to win the war alone and this would have meant the total subjugation of Italy to the German ally. The Nazi Party would have "invaded" the Italian society without doubt [something similar happened in the last years of the war, when the Nazis got the control of the Social Republic created in the North of Italy, there were even Italian Waffen SS ...]. So it was pivotal to take part to the conflict. And Hitler required it: Germany needed Italian Navy to obtain the control of the Mediterranean Sea. But Italian Navy, despite it was a good Navy, without carriers [because of an odd stance of the admiralty who didn't appreciate carriers ... better battleships!] wasn't able to obtain great results. For example Italy never conquered Malta.
So ...
No, I don't think Italy had realistic possibilities to stay out of the war.
In case Italy remained neutral, probably Hitler would have required Rome to allow the German Armies enter Italian territory and to use Italian military infrastructures [like US ask Italy to do in case of American military operations in the Mediterranean region ... remember Yugoslavia, just as an example].
Yes, as I've said above, the Fascist Party played a pivotal role in persuading Mussolini to make Italy join the German military effort.