They will rot away, or the rain will wash them away.

Rain will not wash them away, but they will eventually become part of the accumulated organic matter in those places that helps support new unwanted plant growth. You could take your garden hose and with a straight stream clean out the accumulated soil and organic matter in those cracks which will help keep new growth way longer than the plant poison will.

kimmq is kimmsr

Since the product has a residual affect for up to one year, I would not purposely try to remove the soil that you sprayed. And any sprayed plants that you choose to remove should go in the garbage can, not the compost pile. That is my educated opinion-The label doesn't seem to address that.

Then when the vegetation starts to grow back, you could try to wash away the soil and debris as a method of control. But since you already sprayed, let it work.