If the dent was deep enough to hit the internal components, it probably would have resulted in more than a slow leak. The pan is a very thick and solid piece of metal. The other interpretation is that a slight dent along the pan edge caused a slow leak, and that slow leak over a long period of time led to dangerously low fluid level, hence the concern over damage to internal components (like solenoids and stuff as mentioned above). Did the mechanic indicate how much fluid was added and what type? There may be clues on the invoice.
Either way, if the dent wasn't shown to me at the time, I'd want to put the front wheels on ramps, remove the belly cover, and take a good look at the pan. I'd also want to get an OBDii device and app to regularly scan for codes. I started recently to scan on each drive and found occasional codes that went away on their own or stayed away after being cleared. They didn't trigger the CEL. There are problems lurking below the surface.
If the diagnosis was from a trusted mechanic, then they would be in a better position to advise whether it is safe to continue driving until the replacement pan arrives.