Yes that's possible. You can insert metadata using CB Auto Actions on any trigger infact. For activity this would be on the activity_onDisplayActivity trigger, which has the following variables.
Code:
[ &$rowStream, &$row, [
'title' => &$title,
'caret' => &$caret,
'date' => &$date,
'message' => &$message,
'content' => &$content,
'media' => &$media,
'header' => &$header,
'footer' => &$footer,
'menu' => &$menu,
'compact' => &$compact,
'obscured' => &$obscured,
'isDetails' => false,
'isNew' => $isNew,
'isRow' => $isRow,
'isModal' => $isModal,
'isInline' => $isInline,
'isSimple' => $isSimple,
'isEmbed' => $isEmbed,
] ]
var1 is the stream object. var2 is the activity object. var3 is an array of all the layout data.
Now you'll need to be a bit careful here since this trigger is applied anytime an activity entry is rendered. So you'll need to condition against some of the layout data. Specifically "isRow" as that indicates a single row is being rendered. You would do this with the following condition.
Field: Custom > Value
Custom Value: [var3_isRow]
Operator: Equal To
Value: 1
Now you can output whatever metadata you like having access to the stream, the activity, and all its layout data. Additionally whatever Joomla menu item metadata you've configured should also be applying automatically.