If you are going to Rome with a high speed Frecciarossa train, those trains have reserved seats only like airplanes, so they won't be packed with locals going to work, everyone will have his/her own seat, and nobody will be standing unless going to use the bathroom. You can't get on those without a ticket with a specific reserved seat.
There are very few workers that commute via Frecciarossa, being a rather expensive train which besides makes no stops between Florence and Rome, and there are very few residents of Florence who would commute daily to Rome, 200 miles away (or viceversa). There are however business travelers on those trains, like there are business travelers on airplanes.
If you are asking if there are times when those high speed trains have more passengers than others, I would say that the early morning or evening (after work) trains have more passengers than middle of the day trains. That is because many business travelers travel during that time to make their meetings and then return home after work. Tourists also tend to move to the next city with the early morning trains.
The only trains that can be truly packed with locals going/coming to work are the Regional trains (those that make multiple stops). Those can be packed with people standing (seats are not reserved on those trains, but are on a first come first served basis like a subway or commuter train in the US). Also in that case there will be more passengers during commute time, but not in the middle of the day