Yes, I think that's a good explanation. One question it raises is ambiguity in thinking of QM via "many worlds". What constitutes a "world"? If we put a system into a coherent superposition, does that mean there are two worlds? Then if we transform it back into a pure state, has a world gone away? What about the fact that whether it is pure or in a superposition depends arbitrarily on the chosen basis? A pure-state vertically polarized photon is in a superposition of states using the diagonal basis. How many worlds are there, two or one? This interpretation can't be more than very metaphorical - it is "as though" there are two worlds in some sense.

Or do we only count a "world" when we have (some minimal degree of) decoherence leading to permanent separation? That way worlds never merge.

The explanation of QC in terms of MWI will vary depending on which interpretation we use. In the second one (worlds on decoherence) the explanation is pretty much the same as in any other interpretation. We put a system into a coherent state, manipulate it into a pure state, and the measurement doesn't do anything as far as world splitting.

But in the first interpretation, we want to say that there are many different worlds, once for each possible value in the quantum registers. Then we change the amplitude of these worlds, essentially making some of them go away so that there is only one left by the time we do the measurement. It's an odd way to think of worlds.