Can group messages be permissions based?

Lisa's random questions number 37....  Joy

Can permissions be attributed to the ability to leave 'group messages'? 

In one of our private groups I'd like to be able to give the group owners and managers the ability to use the 'group message' feature to post a quick message in the group and have that message displayed in the activity feed. However, I can't see a way of restricting the ability to post a message to just the group owners/managers or specific site roles. It seems that if enabled, ALL members of a group can post a message. 

Is there a way of setting permissions for that feature to just a specific group or site role? 

Lisa 

P.s I have a ton of questions lined up at the moment so apologies up front for being a pain in the coming days! Joy