Typically, no. Some tablets have an option in the settings on how to scale the output. Also, some TV's have had issues with certain tablets at times.
Some apps will blank out the tablet screen and show only the HDMI output, other apps will show the video on both screens simultaneously. I know when I use the Daily Yoga app via HDMI, the tablet screen is just a seek/play/pause and the video output only shows on the TV screen.