Wikipedia says that Ipomea is a large family of over 500 flowering plants, which include many species called Morning Glory, Sweet potato, moonflower, and water spinach.
Many of the Morning Glories contain alkaloids, making them not palatable and possibly toxic. Some say that the seeds of certain Morning Glory species contain psychoactive compounds. Obviously this area needs more research; however, it was enough of a problem that Louisiana banned the production of Morning Glories outside of ornamental purposes.
Plants for a Future lists Ipomea purpurea as not edible, but does address the medicinal or hallucinogenic quality of some seeds.
So possibly edible, possibly toxic. Probably something I will not continue growing on in the future, in favor of better plants, like its cousin Sweet Potato.