a many-worlds question for my philosophical readers

One version of the quantum many-worlds hypothesis suggests that, every time I reach a crossroads at which I have X number of choices, the cosmos splits into the number of universes that corresponds to the number of choices in front of me: if I have nine alternatives, then eight more universes are born such that I, in my universe, select Choice 1 while the other eight Kevins, in their universes, respectively select Choices 2 through 9. (It could actually be infinitely more complex than this, as I discussed in my frothing-metaphysics post over at Kevin's Walk, but let's keep things simple).

Given the above, I have a question, born straight out of the mind of Sam Harris, who has gleefully taken an axe to the tree of human freedom: if there is no free will, such that we're never actually making choices, could this be seen as an argument against the existence of many worlds? In other words, if it takes choice for universes to split into alternate universes, then can such splitting happen if there is, in fact, no choice?