Would a Periapt of Proof Against Poison nullify the effects of alcohol?

The description of the Periapt of Proof Against Poison (PoPAP) says that “poisons have no effect on you. You are immune to the poisoned condition and have immunity to poison damage.”

So I’m wondering if a character could get drunk while wearing a PoPAP? There’s no “drunk” status condition in D&D 5e, but drunkenness is caused because you’ve consumed enough alcohol to poison yourself, however slightly. Also, does the wearer of the PoPAP know they’ve been poisoned? Like for instance, if someone put spider venom in their food, would they know the food was poisoned when they ate it?