Yes, the single boarding pass is valid for both segments the direct flight. Even if they use a different plane of the same type (ex arriving on an A319 at gate A9 and leaving from gate B10 on a different A319), the boarding pass will be valid and they can scan it for reboarding with no problem.

If it's scheduled to be a change of equipment (i.e. flight 719 FCO-PHL is a A330-300 but flight 719 PHL-DCA is an A319), you'll get two boarding passes in that scenario.