Can a scrum master operate in the role of Scrum Master and PO or Product Manager at thesame time???

An organization I was interviewing for as a Scrum Master started  their introduction by telling me that my role will be that of a scrum master and Product Owner at  the same time, i.e. apart from facilitating Scrum Events, removing impediments, shilding team from outside distraction, and organising team to be highly performant etc,  the Scrum Master will also be managing the Product Backlog, be point of Contact for external communications e.g.