The internals won’t recharge inside the camera, solar or no. There’s circuitry to prevent that because current to alkalines or lithiums would be very bad.
You can run other types, but you risk leakage with alkalines. I’ve seen some people report that they’ve run lithiums with an external battery setup, but I’ve also seen people say that the lithiums died and the external wasn’t used.
I only run rechargeable/internal with external setups, with or without solar.