In short, no. USPS has many types of boxes and it can be complicated to know which labels can be used with which boxes -- and easy to get in trouble. Because of this we don't recommend using USPS-provided supplies with any Curtsy label.
If your item is over 1 lb, and it says "Priority Mail" on the label, you can use USPS-provided Priority Mail boxes as long as they don't say "Flat Rate" on them.
However, most items on Curtsy are under 1 lb and ship via USPS First Class -- these cannot be shipped with any of the USPS-provided packaging.
You can always message us or ask anyone at the post office for guidance if you're stuck!