Yes, you can.
Here's what I would recommend you doing. Assuming you are on 6.5, but this should work for 6.2 and 6.3 as well.
Go to the Web UI for AppMon. Its usually the server name on Port 9911.
Once here, pick the 'dynaTrace Self-Monitoring' profile. This is an out of the box profile which monitors the AppMon deployment itself. Now, create a new dashboard. I would recommend adding an alert tile and selecting the 'Collector not Connected (unexpected)' incident. This will go red anytime the Collector is offline.
I would recommend taking this one step further and adding similar tiles for Performance Warehouse, Frontend Server, and other similar incidents. This will allow you to create a single dashboard monitoring the availability of all key components.
Hope this helps,
One more idea to check connectivity status:
Create one incident rule by selecting the measure "Number of agents" or " connected agents" by settings the threshold to total number of agents (say 55), scheduling frequency is 1 hour (long time frame).
This will trigger alert when all agents get disconnect ( say 55 get disconnects suddenly).
All agents gets disconnects mainly due to collector goes offline.( 99% probability)
Create web dashboard and add the incident rule created it turn RED if it violates the threshold...
All agents disconnects abruptly... Nothing but collector goes offline...