Unless it got soaking wet, and/or had repeated very wide swings in temperature, should be fine.
I have fired some WWII-vintage ammo in my Springfield 1911's...all went Bang! the first time. Same with some late '50's M2 Ball .30-06.
The old 'waxed paper' type shotgun shells would sometimes absorb some moisture and swell, making them difficult to chamber, and sometimes not fire.
I have recently shot some plastic hull shotgun ammo from the '70's. (Dated as such by Wincester & Federal, according to lot numbers.) Again, all went BOOM! on the first try.