I see, so "if there is convergence" is not a point of theoretical uncertainty, but something that depends on the way the AIs are built.

Well, it is both. Convergence in the sense of "outcome is independent of the starting point" has not been proved for any AI/updating architecture. Also, I strongly suspect that the detailed outcome will depend quite a bit on the way AIs interact and produce successors/self-updates, even if the fact of convergence does not.