I stained one birch shotgun butt stock probably 10 years ago, didn't bother to neutralize, and it has long since turned nearly jet black (probably did it within only a year or two). I have stained a beech rifle stock about 5 years ago, and also didn't bother to neutralize, and it has continued to grow noticeably darker and darker over this time.
Linseed oil is hardly waterproof (especially if it isn't dry). It could still be neutralized.