I'm running Mate (LTS) on my new RPi3. Everything is working fine as long as I plug in an Ethernet cable. If the cable is removed, my screen (connected via HDMI without adapters) immediately turns black. As soon as I again plug in the cable, it turns back on.
// an empty Ethernet-cable does not give me the screen, only a cable with a connection helps (But a wifi connection has no influence)