+P loads can be loaded in regular .38 Special brass without issue, however you'd need to make sure the ammo doesn't end up in a gun only rated for regular .38 Special rounds.
+P headstamp means the original factory load was +P. There is small variation in brass between various manufacturers, different plants / lines with the same manufacturer, and probably small variations over the decades. Any of these variations could be more significant than the variation between regular and +P brass.
FWIW +P .38 Special loads are only about 15% higher pressure than regular .38 Special and both are considered low pressure rounds.