I think you mean the miniHDMI port on the Tablet itself. There's no HDMI port on the keyboard/docking station.
Yes. I connect to an ASUS 24" VH242H monitor that has an HDMI port and is rated at 1920x1200. The TF101 video and audio output pass to the monitor fine. I get full screen, high quality video. I use MX Video PLayer to play various video files. The videos fill the monitor fully and the quality is great.
The one exception is Google Rented Movies. I can't get those to play on ANY external device, including a DELL Projector, the ASUS monitor or any SMART HDTV's.
All I get is audio and a black screen on the devices and on the TF101. Without the HDMI connected, the movies play fine on the tablet itself when the HDMI cable is not connected.
But I am not alone. I have seen several posts on various forums from TF101 users who experience the same problem with rented Google movies, and is doesn't matter whether you stream right them after purchasing or whether you download them and play them later, offline.