Sure, you can always just run the baseline simulation and compare error rates. You can also do fancier analyses to get some rough idea of robustness and maximum error rates (over your particular parameter domain).

Would this integrate with e.g. Measurements.jl?

The error propagation won't be through measurements, because that blows up linearly. There's other approaches which give much more promising results.

From an implementation perspective of course, so you can get error propagation on the baseline simulator. For the actual ML part, you'd get Measurements complaining that it doesn't know how to propagate bounds through the surrogate. You can do some estimation of what that propagation would look like, but it's a research project.