Yes this is correct for the CGOET, you need the 3 contacts on the steady grip/action cam for the camera and gimbal to power up. I see no reason why the CGOET camera/gimbal would not work fine because it is approximately the same configuration as the CGO3/+. However I do not think you will be able to use the Smartphone app to view the video or to control the camera functions. You will likely need to use the ST16/S to see the video and set camera functions, and start/stop recording. However you will still not have control over the gimbal, it will only self level, no Tilt/Pan control. Pan control becomes manual which is expected with a hand grip, however Tilt control on the grip may not control the gimbal of the CGOET -it does not control the tilt of the C23. You wont be able to tilt the camera up or down manually because the gimbal will always try to remain level.
The C23 & gimbal is physically too large for a Steady Grip/Action Cam handle. It will engage the mount and power on, but the built-in mushroom antenna interferes with the top of the grip battery compartment and almost totally compresses the dampers when installed and prevents the gimbal from operating freely -actually from operating at all.