Oh no, you'd not be expected to carry your luggage around to sightsee. You'll leave the hotel, head for the bus, then off to the next thing on the agenda. If your tour makes a sightseeing stop between leaving the hotel in the AM and arriving at the next one, you'd just leave your luggage on the bus. You might also leave your day bag on the bus if you're just stopping for a couple of hours.
For instance, on the Heart of Italy tour you go from Volterra to Cinque Terre with a stop during the day in Lucca. We had a walking tour, time to walk or bike around the wall there and grab a quick lunch. The bus driver stays with the bus and your luggage stays in the luggage bay.
Do heed the pack light mantra. If the Italy tour you choose includes Venice you'll have to manage your bag on and off the vaporetto and over all the bridges in Venice to your hotel. The bridges are steps not ramps so you can't pull a roller bag up and over.
If it includes Cinque Terre and you are staying in Monterosso al Mare, you'll leave the bus in Levanto and take a short train ride to Monterosso. You'll have to manage your bag on/off the train and to the hotel.
If you can tell us which tour we might be able to give you specifics.