The pressure on your submarine becomes greater as it goes deeper, and the amount of pressure is the hydrostatic pressure exerted by the water. So that part is true, -yes, water can and does exert pressure.
Will it implode if there's a "structural fault?" well, it depends on what kind of fault, obviously, but yes, eventually the submarine will implode, whether there's a fault or not, if it goes down beyond its "design limit" depth, because the pressure simply gets greater, and greater, and greater. All subs. are built to a design strength limit, and can (sensibly) go down no further than that.
In your "structural fault" case, the sub's design limit presumably is compromised, and so implosion will occur at a shallower depth than if it were perfect.
So, "Yes" water can exert pressure, and "Yes" you sub will implode.