I did a little research, the main thing I gather is that upon entering Italy, the authorities normally would stamp your passport.  In your case this was not possible.  I could not find any specific restrictions for travel in Italy.

Here is some contact information for the U.S. Consulates in Italy, though, they would be able to alleviate any concerns you may have:

• American Consulates in Italy

• CONSULAR AGENCY VENICE:
  •  
    • Mailing address:
      Venice Marco Polo Airport
      General Aviation Terminal
      viale Galileo Galilei, 30 – 30030 TESSERA (VE)
      phone: (+39) 041.541.5944
      fax: (+39) 041.541.6654
    • U.S. Citizen Services
      • only by appointment
      • e-mail: veniceconsularagent@libero.it

The obvious issue is retrieving your passport prior to travel back to the U.S. or to other countries in Europe.

Have a Safe and Enjoyable Trip !

Ciao,

"Java Dave"