My gut feeling says that statistically, even just going from one impact to two impacts being likely would require an immense density of satellites, let alone having more collisions than that.
Then there's also the fact that every impact would have a loss of kinetic energy (because it gets converted to heat as the objects deform), which would also make a reduction in orbit likely.
If the debris keeps fragmenting, which maybe could increase odds of impact, the remaining kinetic energy would be divided over each object. The smaller the debris gets, the more drag it should feel too, because of the square-cube law[0]. So that too would only make it more likely to deorbit.
