Sure! It's important because +2 to Con grants +1 current and max HP per level. Since he's got 1 HP left, if he was 1st-level, then taking off the amulet entirely causes him to get all kinds of dizzy (staggered at 0 HP). He can react enough to put the amulet back on.
If he's 4th-level, then taking off the amulet drops him to -7; he's unconscious, bleeding severely, and mostly dead (but slightly alive!). At this point, it's too late.
I'd probably do something similar to Plane Sailing: as he begins to take the amulet off, he notices that the scratch on his arm starts bleeding again, he starts to feel faint, and begins to get a nasty headache. If he takes it off anyway, well, then, see above.