Will my manager be able to see specific responses for their team?

Your manager will never be able to see data by person; all they will ever be able to see is aggregate data for your team, and to view that they need to meet a minimum number of responses.  
Some organizations give managers access to their team's data in aggregate, while others choose not to give managers access to survey data at all. Contact your HR team to learn whether they will provide managers access to team data.