It might boost conversions in two ways: 1. Make people convert now because they don’t want to chance it. 2. If they come back, they might be more easily converted.
Tell them that they can buy the product today, or return tomorrow and get it cheaper (or get a bonus), but there is a risk. You only offer a limited number of copied, and if it runs out today, then anyone who waited for the next day will mot be able to buy it at all.