Do I have to install the BCS plugin on every machine to be able to open a scene with a BCS node in it?

Yes, the BCS plugin has to be installed on every machine that needs to open a scene with a BCS node in it. In general, when a script or plugin just alters something in a scene, from simple rename operations up to automated rigging systems, it doesn’t need to be present on a machine in order to open the “altered” scene. Plugins that create and register new nodes in Maya, however, have to be present.