I don't know, during that time there had been quite a few invasion in Italy which could have a negative effect on the economy, but Italy, especially the north part is probably in a very good position to become very wealthy.
Italy was very rich until the Byzantines lost it(a second time). The wars in the 500's reall destroyed Italian economy. But they would still be a very rich european region, especially in the north, and down to Rome.
Sicily too, but was ravaged even more by wars, swapping lords like socks.
Btw, I know medieval society was better than what we previously thought, but remember that the medieval period is from ca 450- 1453.
I wouldnt say most of Europe surpassed the Romans until much much later(I believe 17-1800s approx, in terms of laws, civility etc etc), and european lands which wasnt a part of the Roman Empire, and many who where didnt have, or lost a lot of know how and state structure, technology etc. So we are talking about a thousand years scope here, and I confidently would say no one surpassed the Romans at least until the 1200's.
The Byzantines however had brain surgeons, free bread, horse races, lawyers, the first modern laws, aqueducts, roads, schools, a hierarchical ladder, state of the art architecture etc etc, and libraries with ancient knowladge and battle/strategy handbooks for officers etc in this period.
It's funny that the renaissance began after the fall of Constantinople(Greek refugees to Italy)...