Italy had no interest to destabilize Libya, in fact it had a good relationship with Gaddafi. It intervened only after US and France started, as a sort of damage control, since France was set to replace the Italian-friendly government with a France-friendly one. (I will add that US, France and Egypt are _still_ making a mess in Libya by providing weapons to the opposition to the UN-recognized government).

In any case, I don't think it would change too much, since most of the migrants are not Libyans running away from the civil war.