I had close to the same question a few months ago.
Artillery doesn't impact CV much, if any. What it will do, on the defense, is disrupt and break up the attackers, causing losses, but more importantly, disrupting the attack, causing moral losses, and causing a temp reduction in the attacker's CV as the artillery shells land.
On offensive, its close to the same thing but you need more artillery to get the same impact, especially if the defense is fortified or in a city.
And without a lot of artillery - read Artillery Divisions - supporting the attack against the Germans, the Soviets will have a very hard time dislodging a decently constructed German defense in 43 and beyond.
The Germans aren't in the same shape as the German Infantry divisions have a lot of organic artillery support. But if you apply the right artillery SUs to the Germany attacks on, say a city, or fortification, can make a difference on how many losses you suffer or how many the Soviets suffer.
There is a lot of debate on how much artillery support the Soviet army/fronts should be assigned in 41. And you just have to come up with a style that fits your type of play. I standardize my assignements at usually two RVGK battalions and one 41 battalion. This provides the maximum amount of guns at different ranges for a minimal amount of manpower.
However, some of the guys here think that way too much and do a minimium assignment. Just whatever is avaliable at the start after they reassign the artillery to the front. I want to kill as many Germans as possible, so the extra artillery worth it, but I'm not a top ranked player. And if you are getting pounded by a good German, you just may not have the manpower, the AP, or ARM pts to do these kind of assignments.