It really might, or it might not...There are pretty wide differences in manufacture and quality with all factory mass-produced rifles. What would you like to do with it at 500 yards?
Maybe the one you buy would, or handloads might get you there. For deer, or 8 inch targets, I would say you will definately need handloads unless you get a blessed one, or have it rebarreled.
If it shoots 1.5 moa which is very decent, and it maintains it all the way to 500 yards without degenerating on the way, you can play the wind properly to hit your POA, you'd be having 7.5 inch groups at 500 yards.
The 7mmMag will have no problems getting out to 500 or more yards, but a typical hunting rifle will have problems hitting anything meaningful at that range. I have seen lots of hunting rifles that shoot in the 1 to 2 moa range. Some shoot better but they are few and far between. I have seen some shoot far worse too. It’s just the luck of the draw. If you had the opportunity to try one out before buying that would be about the only way to know for sure. What are you expecting to use this gun for? Once you have determined what the primary use will be you can make a better decision as to what is required to do the job.