No, they're inside the Roche Limit.

Roche Limit

The Roche limit is the orbital distance at which a satellite with no tensile strength (a "liquid" satellite) will begin to be tidally torn apart by the body it is orbiting. A real satellite can pass well within its Roche limit before being torn apart.

Saturn's Roche limit

The Roche Limit is essentially the distance at which a body will be torn apart by the gravitational influence of another body acting upon it.

What happens? It all depends on the relative size of the two interacting bodies, and their relative compositions.