The pin being off centre will not affect the firing cycle
In a sporting rifle it would have little bearing on “minute of deer accuracy” unless as previously stated the strike is on the edge of the primer which would be dangerous as pierced primers may result
From an extreme accuracy perspective, an eccentric firing pin may cause inaccuracy
I say this because the non central (eccentric firing pin) may drag or strike the bolt tube and lose force / jam and be inconsistent with firing pin strike on the primer
The bolt may also be eccentric to the bore line causing uneven forces to have a negative effect on the action during the firing cycle
It’s been well documents by H Vaughn in his book Rifle Accuracy the Facts about the negative effect on accuracy the bolt lugs being misaligned with the bore and the subsequent forces causing the barrel in the tenon to move unevenly during the firing cycle under these situations causing the odd flyer or unexplained fall of shot
The above wouldn’t be something to worry about in normal sporting applications - I’m using the above as an extreme example as building accurate rifles is my goal whenever I take on a commision
Miki’s inages shows two set of cartridges fires with large and small diameter firing pins - no issues really with either, though evidence of over pressure with ejector wipe marks,,,,,,
Hope that helps