Like mentioned it depends on what your accuracy requirements are. If your shooting competition and are looking for one hole groups then yes it will make a difference.
If your like me, and are looking for an accurate hunting load that will simply give you an inch or slightly less groups on average, then it isn't such a big deal. I do however full length size all of my rounds, especially in .308 since I purchased a bulk order of once fired MG cases. When I first got them I found that the standard FL die simply didn't cut it and I had to get the small base in order for them to fully chamber.
After I sized the whole lot, and believe me that wasn't a fun exercise, they all chamber fine, but I still FL size them after shooting to make sure everything works proper in the field.
I worked up my loads using H-4895 and these cases and have also used Win, Rem, Federal, and Hornady as well, with the identical load and they will all combined shoot into 2" or less at 100yds. For me this is fine as I normally don't shoot this particular rifle much over that anyway. Even out to 250yds however, they all stay within about 3-4" so again plenty good for my concerns.
That said I could probably spend the time and effort to shrink the groups down if I wanted to using each case brand individually, but again, the one load shoots good enough in them all that I don't sweat it.
In my 25-06, brand name means nothing, simply load them with the proper charge of RL-22, and seat the 100, 110, or 115gr bullet to the proper OAL and go shoot or hunt. The only time this particular rifle has had an issue with grouping this load was when the factory stock started to warp. I changed that out and haven't had an issue with it since.
In my 7mm Rem Mag, I use Remington cases almost exclusively as for what ever reason it simply doesn't like anything else on a consistent basis. With the Rem cases it almost gets boring shooting groups at 200yds, throw the same into any other brand and no dice. Even working with the same combination from a start load to a top end it simply will not group as well. With Rem cases I can switch powders or bullet weights and pull the group into a nice little cluster with not much fuss or muss. Using Win or any other brand, it WILL get there, but it is so much more of a pan to do so I won't even bother anymore.
So as mentioned if they shoot up to your expectations with your loading process then your good to go. If not try something else.