Practically speaking, I think programmers have seen that the colors actually max out at 3841 simultaneously displayed, so no. Besides, it would be an unnecessary pain to use all available at once anyway. Some of the most beautiful arcade games used less than 200 simultaneous colors displayed at once in typical scenes. It's more about palette options and just enough simultaneous application to achieve versatility for artists, rather than simultaneous color numbers for their own sake.
Legend of Success Joe was only able to be an exception to this due to its unusual cart design properties of awesomeness that allowed for untold color depth. To this day, nobody fully understands how it was done though.