1998 Pontiac Grand Prix Antifreeze reservoir

All cooling systems are sealed to maintain pressure when the engine is warmed up, and unlike most other manufacturers, GM includes the reservoir in that system. If the hole you're seeing will prevent the bottle from holding pressure, it isn't supposed to be there unless the hose to the radiator is disconnected or there's supposed to be a coolant level sensor in there. To know for sure I'd have to see a picture of it.

That hole is not a break or a defect. It is manufactured, and is most likely an overflow port. Your car uses a radiator pressure cap similar to all other car brands, so the reservoir is not part of the pressurized part of the cooling system like on some other GM cars. You should have a hose attached to the cap for the reservoir, and under the cap that hose extends down to the bottom of the reservoir. That is so it can suck up coolant all the way to the bottom when the engine cools down and that coolant contracts.