Not for me
Maybe Im just weird, or maybe just this voice doesnt do it for me, but I started relaxing less and less the more he repeated the "every time I say deep sleep..." line. I also got increasingly bothered by him always ending things with "doesnt it?" and saying "thats right." The repetition was irritating me so much I couldnt get past the first ten minutes of "Sleep like a baby", but it seems to work for other people, so, if you dont mind the repetition, then all the power to you.
Sage of the Rose about
Deep Sleep and Relax Hypnosis, v1.2