I was in Rome a year ago this week, with forecasts for scattered thunderstorms each day.
On the day of our arrival it was clear until mid-afternoon, when cumulonimbus clouds started to form. Around 4 pm there was an angry, violent-looking sky that was a perfect backdrop for visualizing a chariot race in Circus Maximus (here). There might have been heavier rain elsewhere, but the only precipitation we had that afternoon in the central city was a light drizzle (here). The clouds dissipated for a pleasant evening.
The next mid-day clouds again gathered (here). Just as we entered the Church of St. Peter in Chains at 3 PM, heavy rain began. By the time we finished our visit in the church and went back outside, the rain was tapering off. That was the last rain we saw for the rest of the week.
Bottom line -- storms like that tend to be hit-and-miss, and are usually not a major impediment to sightseeing. As mentioned above, they can be refreshing in hot weather, and will certainly lend drama and interest to your photos.