The Product Owner duties make up a full-time job on a Scrum Team. The Product Owner should not be a manager, a developer or have any other partial duties outside the role of Product Owner. This focus allows a Product Owner to complete their duties with complete focus and commitment to the success of the Product. Of course, in the creation of a Product and its vision, there are many things that need to be done with customers, users and other stakeholders, not just working with the Scrum Team directly. If the Product Owner has other duties outside of Product Owner duties, then one or more of the Product Owner duties are compromised, the Product Owner job is not being done and the team suffers. An individual who feels unable to serve as a full-time Product Owner should not accept this position or should work with their management to enable it to become a full-time position.
To learn more about a Product Owners duties, visit the Scrum Team Assessment.