Yes, it can be done. I just did it (as Egypt, obviously) on a normal size Continents map with 8 civs and 16 city-states, on Settler difficulty. I had one-city challenge turned on as well. Had to restart a dozen times or so to find a city site on the coast, on or next to desert and within two of a mountain, which is the site you need for this. To get the different ideologies you need to have enough votes in the world congress to get anything passed, which is easy after a while because you're allied with all 16 city-states, and then get the next ideology you want voted in as the World Ideology. That will cause enough unrest that you can switch to it, then next time you vote to repeal it, and then next time you vote for the next ideology. I won a cultural victory before getting all the wonders, and could have had a diplomatic victory as well, but kept on going and finished the International Space Station in 2040.