Wouldn't it be interesting to "watch" that process in action?

(Of course, from what I understand, it cannot be observed without causing it to settle into one of its many states, correct?)
Well, the gist of Many Worlds (or technically, the Everett-Wheeler interpretation of quantum mechanics) is that the particle doesn't really settle into a single state at all; it exists in all states at once, but the universe reacts to each one separately. You, the observer, also exist in many states at once, but there's no interaction between the states, so each facet of you perceives itself as though it's in a universe where the particle "collapsed" into a single state. Harry explained how that works on pp. 310-311 of
Places of Exile.
(And in the other interpretation Harry discussed, the one I favor in real life, the particle still exists in all states at once, but the many particles making up the brain or measuring device react individually to it by going into different compound states that average out to a single macroscopic state, so the brain/device, and by extension the universe, reacts to the particle
as if it settled into a single state, even though it didn't.)