Sure, societies that don't have the concept of currency. The inhabitants of the Sentinel Islands for example.

Some other societies have different ways of measuring authority and delegating power, but in general currency is more efficient and if they have to interface with the rest of the world then money will be critical. That's why money is usually a proxy for power.

Is it even possible for money to not be power? Like, how do you separate purchasing power from influence power? Purchasing is a very easy route to influence.