No. Nobody considers red blood cells to be prokaryotic, perhaps most importantly because they are _part_ of a eukaryotic organism. Red blood cells begin life with the full complement of organelles, including a nucleus and mitochondria, but our RBCs shed their organelles during maturation. In actuality, though, only mammalian RBCs lack nuclei; other animals' RBCs still hold on to their traditional eukaryotic characteristics.
As an analogy, apoptotic or necrotic cells don't have intact organelles, but they are still considered eukaryotic.