yes, But with a 14" barrel you may need the 3 volt light instead of the 6 volt. I know you need the 3 volt with a 12" barrel, not positive about a 14" barrel.
OK, I'm no expert, but I don't think the size (3,6,9v) makes any difference in mounting, at least on an 870. The only thing that differs externally from one to the other is the length of the tubular battery housing.
Forgot to mention that the reason a 3v makes a difference over a 6v is due to the length of the light. On a gun with a 12" bbl the 6v light extends beyond the muzzle of the gun. Muzzle blast will damage the light. 6v vs. 3v has nothing to do with actual fit. Both will fit all 870's.
IMO one would not want the light to extend any further than the muzzle. My personal preference is for the light to be at least 1" behind the muzzle. I don't have my gun handy to measure out but as I said I know a 6v light is to long for a 12" bbld gun - light extends past muzzle. And may be to long for a 14" barreled gun as well.