Basically, a character with Stagger Lock can still chain the enemy, but once the chain gauge fills to the point where the enemy can be staggered, it just remains there. A different character without Stagger Lock in the party can then push the meter over the stagger point to stagger it. It's not a significant delay unless you are doing something really tricky like taking out a giant turtle's legs before you get killed.
Some Stagger Lock weapons are still worth using, most notably Taming Pole, because of its amazing stat bonuses (or to trigger R:IC if you need it). Hauteclaire and Rigels are also good but only if you are using that character (Light or Sazh) as the party leader. Otherwise there are better options.