Close. It's more akin to skipping the attack roll every round and just rolling damage.
"You miss with this weapon, deal minimum damage."
vs
"You hit with this weapon, deal average damage."
vs
"You score a crit, deal super duper damage."
No matter what, the player knows that they are always going to be dealing damage...so why not let them skip the attack roll altogether and go right to the damage roll instead? Let the damage roll of 1 be the minimum "miss" result, and let the maximum be the "critical hit" that deals super duper damage. "I rolled a 12! I get to add more dice!" or whatever.
"But that's unsatisfying," some folks might say. "There's no risk, it would be dull, etc." And that's the point I'm trying to make.