Your users are going to have an awful time accepting/rejecting connection requests without Manage Actions tab. At any rate, yes there's a trigger for that page. It is as follows.
onBeforeManageConnectionsFormDisplay
You could use CSS or jQuery to hide the tab as needed. Preferably jQuery that calls our cbtabs API as follows.
Code:
$( '#cbtabsmyCon' ).cbtabs( 'hide', 'cbtabnavaction' );