The "Computer Not Reachable" pseudo-monitor triggers an alert when SCOM cannot ping a monitored computer. So, it has nothing in common with broken connection between a SCOM agent and a SCOM Management group. NB! Ping test only starts in response of communication failure (see further), it does not run continuously.
On the other hand, the "Health Service Heartbeat Failure" pseudo-monitor is exactly what you are looking for: it alerts when a SCOM Agent stops reporting back to its Management Group.
I said "pseudo-monitor" because they both are not real unit monitors, but fake roll-up monitors, which have no down-laying monitors -- so have nothing to roll up, but set programmatically instead.
Cheers
Max