Yes, it is possible to disable automatic replies selectively. The email template is linked to a stage and you could have a stage in one team and not the other.

1. Create different teams, with each having its own alias Configuration -> Teams -> Email Alias

2. Create stages for each team.

3. Associate email template and teams to a stage. Configuration -> Stages -> click the stage. 

To view this menu you would require to enable developer mode Settings -> General Setting -> Click activate developer mode (at the bottom of the page)

If you leave the email template field empty then no emails would be sent. Also optimize the stages by adding to applicable teams.

Eg. You could potentially have 2 stages as 'New' one for the teams where you wish send automated emails and 1 for the aliases you don't wish to send out replies.