If your monitor has a video input and and audio input then yes, the DTV converter should work as a tuner just fine. Just remember to go into the converter's setup menu and adjust the audio output from stereo to mono.

Understand that with this arrangement, you will only get DTV channels and not receive any analog channels.

Two more things:

1.) Some HDTV converters have VGA outputs, so they can directly drive an computer monitor at full resolution. (I have an old Samsung SIR-T451 converter box that can do this.) However these converter boxes will not be "coupon-eligible".

2.) Yes, there are a number of monitors nowadays that do have built-in TV tuners. Alternatively, you can also buy TV tuner cards that plug into your computer. You can then watch the video in a window, and use the computer for other things at the same time.