Apple's HDMI adapter? I'm not familiar with this cable / device. Are you talking about the Apple Digital AV adapter?
However, since the purpose of Optik TV Go is to enable you to watch the service you have already connected to your TV, but on your mobile device, it may well be that output from the phone is prevented from being served from the mobile device to a TV. In other words, you can't stream a TV show through a mobile device to a TV, but rather you have to have it first-hand on the TV, or on a mobile device. So while you can take the show with you on your mobile, you can't set up another TV (at another location) through your mobile.
Apple TV will not mirror Optik TV Go, either.