I strongly doubt that any reasonably aged brass will present you a problem.
I have a box or so of Norma .44 mag stuff that I bought new as primed brass back in the mid '60s that's still in use and as good as when I got it.
That said, I also have several pre WW1 '06 rounds that have split in both the neck and shoulder areas, those're dated 1910........no, they're not reloads and carry the original cupro nickel bullet. I presume that splitting is a consequence of not being annealed but can't know for sure. I have seen, and shot WW1 ammo as late as the mid '60's that functioned normally. I have also fired a few .45-70s that dated from the 1880 that did split.
So, does it go bad..........yeah it can, but what the parameters are likely depend on a lot of issues.
Frankly, I've seen some really scary brass failure with brand new Buffalo arms shells, including one that resulted in a complete case head separation!
If anyone's interested in that last, I'll gladly supply the guy who had it happen's PX!!!