Hey OP
If you have a "serpentine" belt? or Jesus belt? (one belt to rule them all), this belt actually drives all other pulleys with in the engine, for all Buick V6 engines and Ecotec engines. This also includes your VR! (Buick). From Harmonic Balancer, (Big Round pulley at the bottom of engine), to this; driving the Air conditioning pump, water pump, power steering pump, Alternator... etc... This belt, if it's on and circulating with in the engine bay, whilst the car is idling? then the belt is not the issue.
"Important" The leak in the radiator, and not having no water or coolant? would be causing the over heating issue and possibly causing other unforeseen issues also!. I would start with filling the over flow bottle. This sits just above the battery, with coolant. Second, When the car is cold fill the radiator with coolant if at all possible. (This will depend on the radiator type you have).
Third!!! Replace radiator!!! Most wreckers may have good condition radiators cheap and may provide a swap if damaged warranty. If you cannot replace radiator please buy some stop leak for your radiator! Supercheap Auto have some relatively cheap stuff that works well, and this could possibly stop irreversible engine, and attached pumps, damage with heat exposure whilst having dry lines when the engine is in operation... Add stop leak to your reservoir (Over flow bottle)... This will be the smartest thing your mate will do!!!
Hope this helps..
Ohh secondly.. If your mate insists that it is a small leak? However, you've witnessed steam etc after a short distance of driving??? This is not a small leak!!!.... A leaking radiator is serious, A car with out and engine belt is serious.. (No power steering? No water pump, no alternator (e.g."No power"), and no A/C bu that's no bigy!)
By no means am I forcing my will on you guys, but I also know not having your own ride can be quite the pain in the arse.... At any rate I hope that you guys get this issue sorted...
Good luckl!