[sj]

4-2-2f.....The ball becomes dead and the down is ended when....(f) When the kickers catch or recover any free kick anywhere, and when the kickers catch or recover a scrimmage kick beyond the neutral zone and when the kickers are first (i.e.before any touching by the receivers) to touch a scrimmage kick after it has come to rest beyond the neutral zone and between the goal lines.

So if they recover it beyond the neutral zone the ball is dead so they cannot advance it. There is nothing that says the ball is dead if they recover behind the neutral zone so it is still a live ball and they can advance it.