Yes, it will, that goes without a question.
But its firepower is not the reason why.
I find it hilarious you can't see it, so let me draw you a clearer picture:
It got the same firepower as T34/76.
If T34 does not have enough firepower to beat P4, neither does another unit with EXACT SAME GUN, so the reason for different outcome is CLEARLY NOT FIREPOWER, like... there is maybe some difference between KV-1 and 34/76 that is not firepower?
Check your excel sheets, maybe you'll find hints on actual reason why one of these tanks almost always loses and other almost always wins despite having the exact same firepower on both.
I am not sure what you are arguing about. Vipper said it is sufficient to win if the P4 decides to slug it out, there's nothing wrong about it. He did not say it is due to a great gun or whatever, he said it is sufficient to pen the P4 often enough to win the engagement. You're just trying to pick a fight, but this is a quite pointless one.
Also you should check an excel sheet yourself once in a while. You now twice stated (even in capital letters for further mockery) that the KV1 has exactly the same gun as the T34 which is not even correct.
One of the problems with the KV-1 (as many other units) is that it get the complete wrong vet bonuses:
Vet1
Unlocks the "Hull Down" ability.
Vet 2
+35% weapon rotation speed.
+30% reload speed.
Vet 3
+20% reload speed.
+20% rotation speed.
+20% maximum speed.
It durability should simply be move to its veterancy since vet bonuses should help the unit in its role.
The Vet1 fits pretty perfectly.
Moving it's durability to veterancy would require a complete rework of the unit including pricing. Soviets already have a lot of squishy tanks, adding yet another one that just gets beefier over time does not add too much to the faction. The general design of the KV1 is good, it just needs a couple of adjustments in my opinion. I find it slightly too durable for what you pay for, especially combined with a SU85.
Vet often improves the role or irons out some weaknesses (like StuG side skirts), but in this case I would say the KV1 should not get any beefier or Axis would have real issues for a relatively cheap tank. I think the reload speed veterancy is not that bad and mainly improves the role as infantry support due to the bad penetration.
Yes, maybe there could be a bit better vet, but overall it's not completely wrong.