Critter, using the TC Helicon to create this harmony will result in vocal tracks that have a certain "canned" or "fake" sound quality to them.

In the example video, this is evident in the resultant vocals toward the end of the tutorial.

However.... you can still use TCH as a tool. Use it to select and create one vocal part at a time or, from the pop up TCH window, lower the volume of the other tracks it generated, and use that track to learn the part and sing it to a new track in real time.

I have not used TCH in my work in either manner. I have however, used my midi keyboard with a piano sample loaded to play harmony notes for myself and for other singers who were having a problem "finding" the right harmony melody. Using punch recording, I was able to get the harmony parts nailed by using this method, every single time.

Another, third possibility is to use pitch correction software such as Melodyne to alter the part. I have used this on a song called Coming Home...On my website>my music>page 2..... on the part "I'll kiss your lips..." in the first section, that part was created by manipulating very carefully a lead/unison vocal part with Melodyne. I don't recall what other harmony parts in that song were done that way but I know that one was.

You can find my music at:
www.herbhartley.com
Add nothing that adds nothing to the music.
You can make excuses or you can make progress but not both.

The magic you are looking for is in the work you are avoiding.