Supposing I play Time Walk when my deck is completely depleted. Putting it under my deck means just putting it down as a deck of one card right? The rules say I don't need to shuffle my discards into a new deck until I need to draw.
Correct. In fact if you are really really savey, once you get to this point you can continually return cards to your deck using Time Raider and Repeater Perfect to try and delay your reshuffle as long as you can and essentially get non stop double turns and have complete control over your draws.