Definitely not, Scrummasters should not be connected to the project at all. Their job goes directly against it, a PM is a stakeholder who will ask for everything to be done immediately, and needs to get stuff done. A Scrummaster should be neutral, and should uphold the process and defend the dev team.
Common scenario:
PM: "I need this task done immediately"
Scrummaster: “This task does not have any definition, and the team is already working on things. Once you have requirements we can discuss options on prioritization for next sprint”
That right there highlights where a scrummaster should be working. Most companies do treat them as neutered dogs though, and don’t give them the power. True scrummasters have the ability to push back on PMs and defend their teams, keeping developers out of it so they can stay heads down. (Less useless meetings)