Yes, solid state amplifier designs don't care whether there are speakers connected or not. Without speakers connected, there is no current flow and no heat built up.
And it also wouldn't care if you had all speakers connected or not. If you have one connected, it will play. If you have all connected, they will all (normally) play.
You said there doesn't appear to be any output transistors or what would look like them. Are there any devices which look like kind of large rectangular flattish pieces mounted on heat sinks? Those would be what are called output modules which contain all the output circuitry in one unit. If none of those are present, it may be that the power outputs are low enough that the output transistors are just normal-looking transistors stuck into the boards.
In any event, both back channels not working would point to something in common with those channels which would normally be a power supply issue. However, being that the front channels work, it is hard to imagine them using separate power supplies for the front and back channels in a unit such as that. Hence me asking about power output modules of which one may contain both back channels.
Doug