I contacted support about how to turn off the “pending messages” feature in G Suite (formerly Google Apps) groups, so I’ll share their response.

The setting to prevent messages sent to groups that are determined as spam from being held can be configured with the following procedure:

Setting Procedure to Not Hold Messages Sent to Groups

1. Access the group management screen (accessible through either of the following procedures)
   
   • Click [Manage] in the upper right of the target group's screen
   • Click Admin Console [Other Settings] > [Groups] > [Group Name] > [Access Settings]
2. Click [Settings] > [Manage] in the left menu of the group management screen
3. Select [Skip moderation queue and post to the group] in the "Spam messages" dropdown menu
4. Click [Save]

The default for this setting is fixed at [Send to moderation queue and notify moderators] and it seems the default setting cannot be changed.

You can only change this setting in each group’s management screen. I hope for future feature improvements.

That’s all from the Gemba.