Can a player survive suffocation with a Periapt of Wound Closure?

What happens to a PC wearing Periapt of Wound Closure while suffocating? I’d like to transport myself using a Homunculus and a Bag of Holding, but I worry about suffocating during the journey.

If I put on a Periapt of Wound Closure and enter a Bag of Holding, will I suffocate to death while inside? Or will the Periapt keep me alive?