Not precisely. There are some programs for inter-subject analysis using non-parametric analogs to t-tests and ANOVAs (3dWilcoxon, 3dMannWhitney, 3dKruskalWallis). These operate on ranks, not via permutation tests.
It is also possible, via 3dfim+, to use Spearman (rank) correlation in the time series analysis of a single task. This ability, however, was purely experimental, and I don't recommend it.
None of these programs use the variance smoothing approach of SnPM.
Your question is somewhat vague, and it would be better to ask about the capabilities you want for your tasks at hand, rather than make a query like "can AFNI do X?" without context.