Planets form from disks of matter orbiting around a star; some moons form from disks of matter orbiting planets. If this were going to happen around Saturn, approximately how much time would it take?
The answer to the headline question is: No. Most of Saturn's rings are below the Roche limit of about 2.5 Saturn radii. Hence tidal forces will prevent that part of the rings to form a (large) moon.
Actually, part of the rings may be caused by loss of material from some of Saturn's moons, as suspected from observations of Enceladus.
Accretion of Earth is still going on. So any number between millions of years and billions of years of accretion time for a planet can be justified. Half of Earth's mass should have accreted within 10 million years, see this paper.
The currently leading answer is correct to say that moon formation inside the Roche limit is unlikely.
However, the disk is evolving due to viscosity between the particles, and as a consequence it "spreads", so that material is able to move to outside the Roche limit.
In fact this is a leading possible explanation for the formation of the inner moons of Saturn - that an initially much more massive ring system underwent viscous evolution and spreading, and that material spread outside the Roche limit was able to condense into the inner moons. See for example http://arxiv.org/abs/1109.3360
Whether such a process can continue is doubtful. Models for viscous disk evolution show that the initial evolution is very rapid and that subsequent evolution is very much slower, so that the rate of mass transferral to outside the Roche limit is now quite small. It maybe that it is too slow to form anything new and that any mass would be just accreted onto existing Saturnian satellites.
It will not happen.
Existing moons have orbits that avoid these matter fragments to become bigger, by posing tidal forces into them.