You can't put it into the Tournament screen, if that's what you are asking (meaning you can't insert it as part of the layout). But the Hand Timer window can be placed anywhere you want, including over the Game window so players can see it. If you are using a multi-display setup and the Hand Timer window keeps popping up off-screen (or not on the display you want), check the Preferences tab and make sure that "Save dialog locations" is checked. Then, open the Hand Timer and move it to the appropriate place, then close the Hand Timer. The next time you open it, it should be in the same place.
I'll add a preference to auto-start the hand timer when it is opened. Should be pretty simple.