Cloud connectivity is only available for connections to the service-mode server, I'm afraid - i.e. the one that remotes whatever is on the console, and would be output to the TV/Monitor.
Given you're running headless, and I'm guessing don't have an X Server started, this explains the fairly uninteresting black rectangle that you are seeing
Given virtual mode server is in effect running a X server and associated graphical applications, I suspect it would be about the same resource-wise if you configured your Pi to boot into the graphical desktop, and connected to the service mode server to show that. Since there's no TV or monitor plugged in, you may need to take some steps to configure the resolution
. That's going to be your best bet for cloud connectivity, I'm afraid.
Hope that helps!