Is it Possible to have a Damaged Radiator without Damage outside of the car?

Probably yes. A radiator replacement is the only sure option. If a collision of any type creates significant movement of the car’s front end materials, the radiator will be affected. This can create immediate and extensive radiator damage.

modern cars have plastic radiator tanks easy to damage in minor bumps. the damage to some of these low speed bumps is not evident until the bumper cover and plastic covers come off. ie hidden damage

there,s bound to be some kind of damage to the grill and if you have AC then it has to get through the condenser to reach the radiator.

Yes

I suppose it's possible... but I can't imagine it happening in a collision without even breaking the plastic grille.

Yes... The impact probably cracked the tank or seam of the radiator.

You bet. Now go tell your folks you jacked up their car.

No. There would at lest have to be scratch left behind.