yes you should add it is more better.

yes but make it a little bit like a 32 clip size and 1000% more amo in reserve than the default shotgun but its going to have some major downsides

What I hate is the how guns in video games seem to have the universal equation of
more ammo = less power. It seems like kind of a lazy way to balance weapons and almost insures they won't be used. For example, look at the Family Business for Heavy. No one uses it because they could just do more damage in a smaller amount of time with the default Shotgun. It doesn't matter if your gun can shoot 500 shots without reloading if it doesn't do any damage. I think a good example of a weapon with more ammo done well is the Natascha. While it does less damage and has a higher spin up time it actually has a buff in the form of slowing people down. While this still isn't a very highly used weapon it is actually capable of being useful, unlike the Family Business (I'm not insulting your family business, I'm talking about the gun) which is completely useless.
(a summary for you TL:DR people)
We need more guns with higher clip sizes that are actually useful.

What I think Stat wise:
Pros:
Never Reloads, all ammo is already in clip
Very High Damage(50% greater)
On Kill:Get 25% ammo back
Cons:
Very slow fire rate
very inaccurate at long range

I agree I think? Slower firing speed, more damage (say +20%, -20% -> net 0.96x dps assuming constant accuarcy) then add in that its a shotgun, so damage scales with the number of pellets that hit ~ r^(-2), and the no reload seems pretty cool. One possible downside is cobining this with a despesner for infinifire, but tbf if you could do that it would work just as well with a minigun just as easily, not a big problem there.

Sorry for the incorerence - summary:
+20% damage
-20% firing speed
no reload
louder than default shotgun, more destinctive lower pitch sound, similar to tomislav.

cough WIDOWMAKER cough NO RELOAD cough USES METAL cough NEVER RELOADS cough cough cough cough cough :)