I have my storefront on Podia. I discovered that Podia does not accept Pinterest code in order to allow me to “claim” it. Will I still be able to add my Podia storefront link to my Pins even though I can’t “claim” it?

Yes you can absolutely add the URL for your store. There should be no problem with that. Since you don’t own the domain on podia, you are unfortunately not allowed to claim the store.