NaHCO3 Electrolysis Products?

I would agree, at least in part, with your hypothesis. The fact that gases were seen at both electrodes suggests that an oxidation/reduction reaction was occurring in solution. However, something else was going on. A blue solution is typical for solutions of Cu^2+. A light blue or blue-green solid could be something like CuCO3 or Cu(OH)2. The precipitate's color could have been modified by the color of the solution. You would need to do more research on the compounds produced and on the deep blue solution to know what was actually happening. Also, you need to capture the gases produced at each electrode and yze those as well. Once you know those things you will have a much better idea of what you actually saw.