Hello,
I'm not sure if I understood the question properly: ssh is the typical way to connect to an instance. You can devise anyway that you like to connect to it, if you upload your own image, for example you could have a vncserver running into it and connect to it via a vnc client.
If the instance is down, there is no way to connect to it, independently from the way you connect to it (ssh or others).
cheers
graziano