No, Costco does not offer a 1-day pass. However, their stores are open for non-member shoppers every day of the year. The only difference is that you can't buy most things or claim any membership benefits while you're in the store.
Costco memberships are valid for 12 months from purchase and provide an invitation to enter their warehouses and use their facilities. Members receive access to the store's huge inventory of discounted name-brand merchandise at warehouse prices.