Decay in the classic sense the way a satellite in the upper fringes of the atmosphere decays? No. It's complicated.
When two objects interact gravitationally energy is conserved. In center of mass coordinates each leaves (assuming they miss) with the same speed they came in on. In the reference system of a large group of such interactions, the small bodies pick up speed at the expense of the large ones. This is the principle of the sling shot effect used by NASA. E.g. routing a probe by Venus to give it enough energy to get to Saturn.
In effect the cloud of mutually orbiting rocks 'boils' off the smaller rocks. SevenEves doesn't make clear how fast this can happen.
Rock has essentially no structural strength compared to it's mass when in large chunks. This is why planets are round. Even Ceres, the largest asteroid is essentially a large lumpy ball. Doesn't take much of a hit to make a big fragment into a large bunch of smaller fragments.
This is important: The rate that rocks are expelled from the cloud depends on:
- How often interactions happen.
- The difference in velocity between each rock and the center of mass of the cluster.
- The ratio of the mass of the large rock to the small rock
Complication: The moon is outside the earth's Hill Sphere. The sun is a stronger force than the earth is.
A rock that comes off the cloud toward the earth has basically one chance to hit the earth before being slung off into deep space.
If all moon were converted to gravel, and spread evenly in all directions, then a "White Sky" would certainly be the outcome. Figure out what fraction of the sphere the earth intercepts, and how long the gravel takes to arrive. All of it arrives at essential earth escape velocity.
(it's more complicated. You have to figure out the effective cross section for the earth because the gravitation will bend paths toward it.)