It is not a requirement that residuals from a robust regression be normally distributed. On the contrary, robust regression techniques would typically be used only if outliers are violating the assumption of normally distributed residuals.
I'm not an expert on these techniques, but I guess that one way to get a handle on whether the robust fit is "doing what it claims to do" is by looking at how much the algorithm is down-weighting the outlier observations. You can see the observation weighting in the output stats.w when you call
[b,stats] = robustfit(...)
