Kind of. Who ever is on call should be able to deal with the issue. Your highest level of escalation should be your engineering manager, VP of engineering or CTO. Your product manager should care about team health checks, and how much you are getting paged, then prioritise engineering time to reduce it. Its about collaboration. If it doesn't work out, maybe you could put your product manager shadow on call too. I haven't ever had to do this, but it could be fun.