Yes; the scenario where the aircraft owner hires a CPL (in practice obviously a CPL/IR) to act as a hired pilot, is very common, and that is how most privately owned jets operate around the world.
It is legal under N-reg (it is a Part 91 operation) and similarly under G-reg where an AOC is not required. This is a principle established worldwide, for many years.
But the pilot should not be supplying the aircraft
In practice the rule is sometimes sailed close to the wind, because many weathy individuals are not knowledgeable enough to choose and thereafter operate an aircraft suitable for their mission profile etc, so they may contract a pilot to locate the aircraft and generally look after it. That is OK but the pilot has to be very careful to not pay for anything himself; the "wealthy individual" has to be the one signing all the contracts and making all the payments.