I know primers can decide whether the load works or not but what about primer depth in the pocket? Could that in any way mess with the accuracy of the load?
Determines whether you're trying to achieve benchrest accuracy. For my needs (tactical/hunting), I don't bother with checking this. However, if you think you need to check this, K&M makes a tool to check this:
It can make a difference especially in random brass that has been fired before. Some primer pockets may be deeper than others resulting in uneven ignition from shot to shot.