It depends on the team and situation. For example, does the team have a strong group of coders but is lacking in management/direction? If so, then the manager should focus his/her time on managing rather than coding. Does the team have a lack of coding skill or just need to bang out a lot of code? If so, the manager can step in and perform more coding tasks. Management is very important and it should be the manager's primary role. However, I chose "yes" because I feel that ALL engineering managers should code in some way or another. Even if it's not production code or in his/her time off, the person should retain his/her coding skills to better understand coding problems that the team faces, be able to step in and help developers, etc...