Hi, yes you can totally backpack in Italy infact Europe is the most backpacker friendly place. I have attached with thie comment two itineraries about how you can travel across Italy in a budget. You can go through it and plan your trip.
Hi! Yes can be done! There are lots of travel agents who organize trips. Just check for it! My friend just finished a backpacking trip across Italy without any agency he found it easy! Touring Turtlez