Model studies suggest that sudden formation of supraglacial debris cover might cause glaciers to advance, by inhibiting ice melt in the lower reaches and altering the driving stresses if the debris deposit is massive enough (basically the weight of the rockfall deposit forces the ice to flow faster). For example, Vacco and others (2010) used a numerical glacier flow-line model with superimposed rock debris to show that a glacier advance caused by deposition of a rock avalanche on the ice will be followed by stagnation of the advanced ice lobe, producing distributed, hummocky deposits quite different from the single moraine ridges typically dated in paleoclimatic reconstructions. This type of rapid advance is different to periodic fast and slow flow that is characteristic of true ‘surge-type’ glaciers.
The cool thing is though that the surface debris cover shows really nice evidence of former surges at the surface of the glacier. For example, look at this photo of the Susitna Glacier in Alaksa: