Product Manager with Engineering Team
Question: "Should product managers be members of the engineering team?"
No. This would immediately and incorrectly imply that product managers reside and have responsibilities in the solution space, with product development.
Although not necessary it is considered beneficial for product managers to possess some technical knowledge so they can better communicate with technical people.
From an organizational perspective, product management is separate from engineering and reports to a product executive.
For more information, please see the "Product Management Organizational Placement" review on page 90 in the Blackblot PMTK Book: Second Edition.