As has been said, most will let you fire the gun with the trigger unset using the front trigger. This is a secondary function, though. The trigger was designed to be fired set. If you look at the triggers in relation to the sear bar, you'll understand why using the front trigger unset is not really the way to go.
When the trigger fires from the set position, all the front trigger does is release the rear trigger, which is loaded on a spring when set, to flip up and smack the sear bar, firing the lock. So, when fired set, it's actually the rear trigger that fires the gun, the front trigger is just holding it down against the spring.
When using the front trigger to release the sear, the angle of the front trigger pivot is well in front of and below the sear bar. The further away the pivot point is both up and down and left to right, the harder it will be to pull. When installing a single non-set trigger, the rule for having a great trigger pull is to have the pivot point even or slightly above and fairly close to the sear bar. This results in a light, crisp trigger pull. The geometry of a set trigger just doesn't give way for that sort of a set up when the trigger is not set.