It's important to note that you're going to be building the district itself mostly for the governor title. This will most likely be your 3rd governor titles although it's possible to get your 2nd from the district.
Futhermore, you can't put a building in the district until you've switched to a tier 1 government. This will be your fourth title so if you're banking on putting that building in the district to get your 4th title -- absolutely don't forget! I've gotten ahead of myself so many times to where I finish the district and then want to construct the building immediately but I can't because I never discovered political philosophy.
Lastly, the ancestral hall's settler bonus ONLY applies to the city that built it. Because of that, there can be certain situations where you want to get political philosophy ASAP, get the district and building completed in your capital, get Magnus to his "settlers don't consume a population point)" ability, and then turn on the +50% settlers card and pump out a settler every 2-3 turn in your capital. I sometimes use this method of "late-game" settling (really the end of the early game when you look at the bigger picture) when I got a holy site or two in my capital and/or second city. Stacking the +50% policy card with ancestral hall can help you play catch up with the other civs.