Can the Dikgraaf-Witten model for a finite gauge group $G$ [Robbert Dijkgraaf and Edward Witten, Topological Gauge Theories and Group Cohomology, Commun. Math. Phys. 129 (1990), 393] be described in terms of the geometry of moduli spaces $\overline{\mathcal{M}}_{g,n,\beta}([*//G])$ of stable maps to the stack $[*//G]$? I strongly suspect the answer is yes, in view of the classical relation between 3-dimensional topological quantum field theories and complex analytic 2-dimensional modular functors, but I'm unaware of rigorous results in this direction.