It can and frequently does. It depends on how much radiant warmth is available and how fast the melt washes away the soot. However, in general, where snow and ice are darkened by soot or other dust, they pick up solar radiation, directly or from other warmed sources, and speed up melting. In marginally warm weather, such as springtime, one commonly finds that a stone or handful of leaves will melt its way straight through a foot or two of snow, while surrounding snow remains unmelted.

This could be an extremely important resource if we should elect to melt the polar icecaps to mitigate the effects of global warming, which currently seem to be cooling planetary temperatures alarmingly.