Without the propagators themselves being monotone they don't have enough to ensure determinism. They also don't have a guarantee of termination. e.g. repeatedly taking Heron steps on a rational interval approximation to compute the sqrt of 2 will continue to ascend the lattice indefinitely, as it isn't complete.
That said, they have many of the elements of the solution. With monotonicity this starts to resemble the more recent work on Lasp, which is being used explicitly to tackle the domain you mention: (strong) eventual consistency: or Kuper's work on LVars, where she drops the idempotent condition fairly early on in the thesis to get closer to CmRDTs, but which then burdens reads in a way that makes them automatically monotone.
That said, they have many of the elements of the solution. With monotonicity this starts to resemble the more recent work on Lasp, which is being used explicitly to tackle the domain you mention: (strong) eventual consistency: or Kuper's work on LVars, where she drops the idempotent condition fairly early on in the thesis to get closer to CmRDTs, but which then burdens reads in a way that makes them automatically monotone.