I don't think so.
Mussolini was incredibly mistrusted in the West after the brutal war in Abyssina.
It's arguable that the West might nominally support Hitler in this war, which would probably mean sitting around and doing nothing.
I find that somewhat...of a leap. The London and Paris elites distrust Mussolini, he is a nasty belligerent dictator but Hitler is a nasty belligerent dictator who is an actual threat to the global order as they understood it...and that was was the assessment of people who quite liked the man, there were already many who utterly loathed him.
Then add in folk memories of Italians vaguely being on "our" side and the all too raw memory of Germany most definitely not...not at all a starter.
And as you point out supporting Germany amounts to doing nothing...so...
There are ways and ways of
helping, a nicely indebted Italy recovering from a small but nasty war could be
helped to remember exactly how much its owes. A little bit of judiciously unequal embargoing would not exactly decide the war by itself but would help push down the Germany economy and rearmament programs and help ensure Germany does not win.
Something as simple as bidding up oil futures in the US-European trade by not all that much and then helping Italy cover the cost while leaving Germany out to dry would have had quite the impact.