Hi Andy, Are you arriving on March 23? If that is the case, by the time you check into your hotel, wash up, and get something to eat, the marathon will probably be over. Linda can correct me on starting time but races usually start early in the morning and I think they usually allow 7-8 hours for marathons, putting you midafternoon.
If I can use the Chicago marathon as a comparison, I think most people leave the next couple of days. The city does not feel any more crowded than usual so my assumption is few visitors stay around for sightseeing. I was actually in Venice for that marathon on a Sunday. And my train back to Rome that night was full of marathon runners and their families.
Maybe you can incorporate watching the marathon into your travel experience? I think it is fun to cheer people on. The Borghese parks and museum look like they are just outside of the route. That would be a great way to spend a Sunday. If you are looking to get out of the city center for the day maybe a trip to the catacombs, Ostia Antica, or maybe get on a train and head to Pompeii?
Have fun on your trip and good luck Linda!
Kristen