No, as long as you follow the right "path" to get there, you won't be going under ANY of the ZTL entrance points (cameras+stoplights) and you will be able to drive in and out of the parking lot without worrying about the ZTL and fines.
The right path to the SMN parking lot: off the Viali di Circonvalazione as you come from the Fortezza, turn right onto Via Nazionale (there are signs witha blue P that indicate the parking lots at the Stazione and at the Mercato Centrale right at that turn) and head toward Piazza della Stazione. As you are about to arrive at the train station, stay to the left of the one way lane (it divides in two sections, one for heading straight and one for turning right) - you want to head straight and take the roundabout.
Right at the roundabout, on the right is the entrance and exit into the underground parking lot.
Do not veer from this route, as you might then end up passing through one of the ZTL gates - then you will be fined! To exit the lot, you take the roundabout again and take the street in front of the McDonald's that turns into Via Valfonda. That takes you back to the Viali.