NOT necessarily.
"Non-corrosive" ammo in US service did not really exist until the advent of the M-1 Carbine. The gas system of that cute little package was essentially "non-user-serviceable"", i.e., NOT meant to be stripped out by the operator., unlike the M-1 Garandrifle.
The .30 Carbine was the FIRST service cartridge to be both non-mercuric AND non corrosive.
Soldiers were (and still are) expected to carry out regular cleaning and lubrication of their weapons, not just fire a few shots and hang it back over the mantelpiece.
Any .303 ammo made with a "normal-sized" brass-cupped large-rifle primer (as opposed to the "big" (1/4" copper-cupped one used on vast amounts of .303 ammo), should be non-mercuric. That does NOT mean that it is also non-corrosive.
IF the ammo in question has a brass-cupped primer, it will be lead-based, and thus a LOT less likely to caused brass cracking. however, APART FROM THE AFORE-MENTIONED .30 Carbine, NOBODY made "non-corrosive" general service ammo until the 7.62 NATO came on line in the 1950s. Be aware that this rule ONLY applies to factories making "official, NATO-spec" ammo. As an example, there was a substantial amount of Czech-made, brass-cased, "7.62 NATO" ammo floating around about twenty years back. It was reliable, reasonably accurate but CORROSIVE, because of the primer composition.
Regard ALL ammo, and particularly military-issue ammo as corrosive until proven otherwise.
New barrels are EXPENSIVE to buy! (Or unobtainable). They can also be expensive to have SWAPPED OVER.
Ten minutes of conscientious cleaning and lubrication will save you a LOT of expense and anguish. Release your inner Irishman, and clean it again a couple of days later; TO BE SURE, TO BE SURE!!