Would it? I always thought they shot roundballs, canister on short distances and that the time-fused explosives were set to explode in some height - which should have made it possible to construct some kind of cover. Did they have impact fuses (that worked)?
Regular approaches had worked for hundreds of years, and the trench was not exactly a brand new innovation just come up with in 1863.
The thing that has to be realized is that:
1) A lot of the benefit that the defender has in a fight in the 1860s is the defensive support of the artillery (meaning cannister) - basically dug-in artillery is a lot harder to eliminate during the fighting, so the attackers eat cannister as they close in. Notice that the attack at Spotsylvania which goes particularly well is the one where the artillery has been withdrawn.
2) To bring up light/field artillery to eliminate dug in artillery during the attack itself is likely to fail because the dug-in artillery has the protection of its works, and will thus win.
3) You therefore need your own artillery to be able to engage in counter-battery fire and
overcome the enemy artillery from beyond the range at which the defending artillery can eliminate your own - thus, long ranged rifles using dominating ground. (In the Union's case this would be 6.4", 8" and 10" Parrott guns.)
4) These guns also fire big heavy shells which can tear up the parapets of the enemy by putting (timed fuze) shell into them (and having them detonate underground) or if the parapets aren't thick enough the shells can go through and burst inside the trenches themselves. Percussion fuzes are better for this, but it's not necessary (though with percussion fuze you can do it even with field artillery to some extent,like the 12lber Armstrong)
Between them, these points mean that by using heavy long-range artillery you can more-or-less remove the advantage the defensive gives, at least over the area the guns can cover. This means you can use what's basically bite-and-hold - eliminate the enemy defensive advantage in a sector, capture the sector, either fend off an enemy counterattack (for which
you have the defensive advantage now) or build up your works on the captured sector, then move your heavy guns to somewhere else and repeat.
For the defender, there are two options:
(1) They can contest each attack by turning it into a fight, which means you are fighting the enemy
outside the advantage of their defensive entrenchments (and can win the attritional fight)
or
(2) They can not contest each attack heavily, which means that you are gaining ground.
This is a system which is kind of "inexorable" - it's hard as all get out to
stop. It's why Lee said in 1862 that "McClellan will make this a battle of Posts. He will take position from position, under cover of his heavy guns, & we cannot get at him without storming his works".
Lee was obliged to make costly attacks to force McClellan away from Richmond rather than let him conduct these regular approaches. In 1864, he doesn't have the assets or position to do such a flanking attack on Grant's supply line.