I have no idea why the error occurs, it's definately a strange one. But it only seems to occur for some people, some times... That makes it much harder to actually work out what's going on, so I can understand your hesitation. If you have the time and energy (and the will to climb the learning curve) you could try to troubleshoot the error which would be a great help to all! To the best of my knowledge no one has had this error occur after the appliance has been working (ie it starts with the error or it doesn't, it doesn't seem to just occur out of the blue after the appliance has been running) although I would strongly suggest if you do use TKL Magento that you set up TKLBAM off the bat. That will allow you to restore to a fresh instance should there be any (further) issues.

But getting back your question...: If you have outside access set up correctly (if you are behind a router with NAT then you'll need to forward the relevant ports and/or if behind a firewall you will need to open the relevant ports - the port details are listed on the confconsole) then yes you (or anyone else with the correct credentials) can access/administer your server remotely. If you don't have a static IP then you will also need a dynamic DNS hosting provider. You can use the (free) tklapp.com domain via the Hub if you wish (you can also use your own domain although you'll need to sign up for AWS Route53 and pay applicable charges AFAIK). There are other free dynamic DNS providers noted in this thread.