It would only make a difference if the display size would be so large as to make the difference between HD resolution (approx. 2MP) and the camera's native resolution perceptible to the viewer.

Please note that if your hyperfocal calculator does not allow for inputting display size/viewing distance/viewer's visual acutance then it is probably assumed that the image will be displayed at 8X10 inches from a distance of 10 inches by a viewer with 20/20 vision. The results will not be valid for any other display and viewing conditions that aren't equivalent.

We must also remember that hyperfocal distance, like the concept of depth of field upon which it is based, is really just an illusion, albeit a rather persistent one.

This question and answers hint around at the issue we're concerned with here: How do depth of field and the circle of confusion relate to pixel size on the sensor?

Paying particular attention to the accepted answer at the question linked above, we can calculate that for images from an APS-C sized sensor such as your EOS 600D (22.3x14.9mm sensor - the vertical dimension for a 16:9 aspect ratio would only use the center 12.5mm of the sensor height) the width on the sensor represented by each pixel on a display with resolution of 1920x1080 would be about 11.6µm. So your circle of confusion would be around 0.023mm (2x the width covered on the sensor of each pixel in the display).

Remember that this assumes our standard display width of 10 inches viewed from a distance of 10 inches by a person with 20/20 vision. Both the display size and viewing distance can be altered by the same factor and the calculation will hold. A display width of 40 inches viewed at a distance of 40 inches, for instance, would require the same CoC because the display (and each of that display's pixels) would have the same angular size to the viewer.

As the answer to the above linked question states:

If the pixels (in our case, the pixels in the HD display)... are sufficiently large enough to limit the perceived resolution of the image, then everything in the image with a CoC smaller than the resolution limits of (the display)... will appear to be equally in focus at the expense of also appearing equally pixelated/blurry. This would occur when the CoC needed for a particular display size and viewing distance is less than twice the width of the pixel pitch of the (display). It would not, however, be a hard limit but instead would the point at which we gradually begin to perceive that the picture is made up of individual pixels that our eyes can discriminate.

Depending on your subject matter and the focal length/field of view you have selected, this answer to What is "Hyperfocal Distance"? may or may not be particulary applicable to your question.

There are a lot of existing questions here at Photography on Stack Exchange that cover hyperfocal distance and depth of field. For more in depth information about how display size, viewing distance, and assumptions about the viewer's vision affects depth of field, which is what the hyperfocal distance is based upon, please see:

Why do some people say to use 0.007 mm (approximate pixel size) for the CoC on a Canon 5DM2?
Why I am getting different values for depth of field from calculators vs in-camera DoF preview?
Where to focus when shooting landscapes?
How do you determine the acceptable Circle of Confusion for a particular photo?
Why do viewing conditions affect Depth of Field?
Why are my pictures blurry even though a DOF calculator shows everything should be in focus?
Why did manufacturers stop including DOF scales on lenses?
Why don't cameras provide you with DOF information?
Automatic Depth-of-Field in modern cameras?