Nah, even in most optimistic scenarios, Italy will take at least 4 to 7 years to take the 4th CL spot back. While their CL results are respectable (won in 07 and 10), their overall performance in Europe has been awful, especially in the Europa League. Their
UEFA coefficients are miles behind the top 3. This year English teams underperform in CL, but with strong showing in last 4 years, EPL should remain top next year at least.
Milan's victory over Arsenal is hardly representative of Italy's state of football. Arsenal's horrible showing made Milan look better than they actually are. Juventus has a strong domestic season but is yet to be tested in Europe. The team is very good from front to back, but only Pirlo, Chiellini, and Buffon are their only truly world class players. Pirlo's age may not allow him to perform well for much longer. IMO they need a better striker to make a mark in Europe. Matri is good but not one you can depend on at highest level. Inter is in dire need of rebuilding the team and will not be a force in Europe again for 3 years at least. The other Italian teams simply don't have the resource to do much.
One only needs to look at the 3/4-empty stadiums and poor pitch conditions in Serie A to conclude that the Italian football is not in good shape. IMO Italy really needs to host a major tournament to upgrade the infrastructure and increase matchday attendance.