Yes; those moons might have lasted as much as a billion years. I have been wondering if the impact of those moonlets might have caused the Imbrium or Crisium mare or some other major feature on the Moon's surface, like Tsiolkovskiy crater.
Another piece of idle speculatiion is wondering what might have happened if those moonlets had been larger, and collided with the Moon with enough force to split chunks off. This might have led to a permanent multiple moon system, as discussed in a couple of threads elsewhere
(
here, for instance)