No, Alarm.com won’t show a Zooz relay as a garage door. It would show up as a light switch.
If the Ecolink controller won’t work wirelessly with your MyQ opener then I recommend using the relay output on the Ecolink garage controller and wire it to a MyQ wall button. Unfortunately, Chamberlain doesn’t put accessible terminals on the wall button contact to connect wires to. But Garadget sells modified MyQ wall buttons with wires soldered to the button contact as described here. That seems like the simplest solution to me.