Given that North Sea oil wasn't enough to make UK's economy larger than Germany's, and the UK had a larger non-oil economy than Italy did, I doubt it.How benefitial would Libyan oil be to Italy? Could it have become the largest economy in Western Europe?
However, a timeline in which Italy's still holding Libya (because they were neutral during WW2) is one in which the economic fallout of WW2 is going to differ significantly from OTL, so trying to predict that is not gonna be easy.