If a smaller battery is put in will it power everything

Battery size and capacity is only important for starting the engine. Once the engine is running the alternator powers the vehicle and keeps the battery charged. It's always a good idea to have the correct battery in the vehicle. It'll last longer and won't make the starter work too hard to get the engine started. HTH. -Jim

Cadillac's use a lot of power. A large battery is my advice.

Two things to look at - Physical size and electrical power. The correct physical size will keep the battery from bouncing around in the battery tray and, therefore, shortening its life. The electrical power it provides will determine if it is capable of properly operating all of the car's equipment. A battery store can help with both and tell you what you need. Look for a battery with a high CCA (Cold Cranking Amps) rating at least at or above the spec for the car.