Time is affected noticeably by gravity only in strong gravitational fields, i.e. in the vicinity of compact objects, so time doesn't run differently in voids from average regions.
Dark matter (DM) and energy (DE), on the other hand, can to some extend be unveiled by studying voids.
The morphology of the voids is affected by the nature of the DE, so measuring the sphericity/oblateness of voids and comparing to suites of cosmological simulations with various implementations of DE can teach us about that.
Studying the change of voids over time can yield insight into the equation of state of DE. Of course, on human timescales a given void doesn't evolve, but they can be observed statistically at different redshifts.
As the DM distribution ("halo mass function") is slightly different in voids from the rest of the Universe, we can also learn about DM from studying the differences.
See e.g. here and here.