Old switch has a loop wrapped around screw. [red wire on brass screw]
To connect a looped wire with one from the dimmer, yes, you unscrew and then cut the loop open, add the wire from the dimmer, twist them together, and cap it with a nut.
Just be sure: confirm that the red on the switch is indeed the hot supply and not a traveler or common. On dimmers the red(s) are switched, and the black gets the hot.