Can we use Apple Remote Desktop to hold internal meetings screen to screen over LAN ? Like Join.me I administer the computers in our office which run a mix of 10.10.5 and 10.11.5.

To assist with problems I use Apple Remote Desktop allot to view and control users' computers. What I tend to do is control their computer whilst on the phone to them and talk them through why it happened etc. 

What i think would be really useful is if I could give users limited access to Apple Remote Desktop to say have "view only" access which was only allowed if the user's computer they want to access accepts and external connection something like "xxx wants to share your screen, click Ok to continue". This way members of staff could have impromptu mini meetings screen to screen which would be very useful. Is that possible ? 

I know I can do it via Teamviewer or join.me but would prefer it to run on the local network via Apple Remote Desktop.
Can you do it?

Yes.  It's a bit sketchy to do this using ARD, but you can.  There is one massive caveat, however.  You will need a license for every client you wish to install ARD on.

From the ARD License Agreement 


  (i) to download, install, use and run for personal, non-commercial use, one (1) copy of the Apple Software directly on each Apple-branded computer running OS X (“Mac Computer”) that you own or control; and
  
  (ii) if you are a commercial enterprise or educational institution, to
  download, install, use and run one (1) copy of the Apple Software for
  use either: (a) by a single individual on each of the Mac Computer(s)
  that you own or control, or (b) by multiple individuals on a single
  shared Mac Computer that you own or control. For example, a single
  employee may use the Apple Software on both the employee’s desktop Mac
  Computer and laptop Mac Computer, or multiple students may serially
  use the Apple Software on a single Mac Computer located at a resource
  center or library.




This can get quite expensive especially when the ARD software is $79 per install.
That, and it's overkill.  You really don't want to give users admin level tools to just share a screen with a group for a meeting.

When I worked in the edu space, one of the products we used was Splashtop.  It allowed folks to share their screens from either Mac or Windows machines.  It was designed to do specifically what you are requesting - allow users to share their screens.  We had an enterprise license but I believe the license for each user is under $20