Yes, they do produce pea pods and peas, but they are NOT edible.
You had asked about the flowering plant called sweet pea, Lathyrus odoratus. The variety of peas grown for human consumption is Lathyrus sativus. Seeds of odoratus consumed in quantities are toxic, while sativus is meant for eating. Use the botanical name for your flowering plant and your person from Lowe's won't be so confused. Anyone who knows anything about gardening would never tell you to eat ornamental sweet peas.