In theory you can, but nobody makes bombs with U233 because it's easier to make bombs in other ways.
It seems to me that the real question for proliferation is not "is it theoretically possible to make bombs with this," but rather "if you wanted to make bombs and you had this technology, would you use it to make your bombs, or would you still prefer other methods?"
It's easier to make them other ways at the moment, because U233 isn't common. But popularize and reduce the cost of this cycle, as well as claiming it's "proliferation resistant" and hence suitable for export to non-members of the we-got-nukes club, may well lead to weapons being made out of it.
Still, if you made a u233 device (and I'm thinking it would have to be a dirty bomb, an explosive seems unfeasible), it would difficult to get it to a target since it's so easy to spot the gamma rays.
u235 is still the way to go, since you can just hide it in a lead pipe in a crate of bananas.
It seems to me that the real question for proliferation is not "is it theoretically possible to make bombs with this," but rather "if you wanted to make bombs and you had this technology, would you use it to make your bombs, or would you still prefer other methods?"