No, this is an outdated idea. Evidence finds that hypnosis is a state of deep focus. You can be in hypnosis without feeling relaxed (watching a horror film) and you can be relaxed without being in hypnosis.

Relaxation is often used to help quieten your mind and enter hypnosis (it's super useful for much of the birth journey) but during transition and 2nd stage you might feel more energised than relaxed...