That's exactly my point favouring GS over GA. By using multiple GS's to lightbulb techs, you only need to research drama and mathematics after alphabet (even mathematics sometimes can be obtained from AI players). You use lightbulbed techs to trade for the prerequisites of the next techs (these prerequisites are CoL, CS, ironworking and metal casting), all the way to liberalism.
Therefore at this point you can slide your culture bar to 100%, which gives you a free hand in whipping the buildings, including cathedrals -- that's about half a dozen more unhappiness points you can sustain. If you take advantage of this, and carefully planned to use small buildings/units to generate overflows for the big ones, you sure can get your cathedrals several turns earlier.
My estimate is that you are about 15 turns earlier in liberalism (100% multiplier) and about 10 turns earlier in first cathedral (50% multiplier), 20 turns earlier in the second cathedral (50% multiplier), and so on. Your culture building will become legendary earlier (that's a 100% boost in this part), and your cottages become towns earlier due to a larger sustainable population.
The effect is so dramatic that I am willing to say: cultural victory is all about when do you slide your culture bar to 100%.