I can't speak for Jerry but an easy way to check the status of the Hamachi connection is
c:\Program Files (x86)\LogMeIn Hamachi\x64\hamachi-2.exe --cli list
Exclude the full pathname if appropriate in your specific case, etc etc. If the VPN is currently off, this will be the result
You have no networks.
If the script picks that up as a response, have it run
c:\Program Files (x86)\LogMeIn Hamachi\x64\hamachi-2.exe --cli logon
And that's the equivalent of pressing the power button on the UI. That way whenever the Hamachi is disconnected for whatever reason, it will attempt to reconnect and log back on without the need of the UI.
For some reason on a new computer that I installed Hamachi on, it seems to randomly decide not to auto-connect (aka "Power" on) and it would be offline, requiring me to press the power button on its UI. Other times it would auto-connect just fine. Apparently this is controlled via a config file some place but the fact that it isn't being consistent was something I found odd. So what I did was create a task run in Task Scheduler to execute that previous command (hamachi-2 --cli logon) set to run "At Startup", set it to run with Administrative privileges whether a user is logged in or not, and set a Condition for it to run after getting a Network Connection with the device that provides internet access. This way Hamachi is already connected to the VPN before anyone logs on (assuming the person doesn't log in fast enough to get ahead of it). From now on I won't have to deal with the randomness of it not auto-connecting or worry about its configuration set to do so.