The policy giving that buff won't apply till you've almost finished the tree. Turn 80-100 or so.
a whole bunch of culture,
not much in it early on
enough buffer-happiness to sell your first luxury,
I get Monarchy on turn 77 after taking that diversion through Liberty. With a pop of 7 at that point, i didn't need any luxes up till then. Granted, i was rushing GL and NC and only had one city.
As for being behind in 2 social policies the rest of the game, maybe, but i usually get more policies than i need to fill one tree before Rationalism becomes available, and i'm not great at finding uses for the first policies in Patronage, Piety etc. I've also been playing as Poland on Empreror a lot recently, they get extra socials which makes my strat more viable, plus that free early worker is essential for winning the GL race.
I made a test game to see how many Beakers per Turn i could get going pure tradition vs liberty/tradition, using a generic civ (as regards social, tech), China.
Build order was
1. scout (tradition game)
2. worker
3. GL
4. NC
5. the rest...
in Liberty...
1. monument
2. scout
3. granary (writing wasn't finished yet, so i had to build something.. it only delayed start of GL 3 turns)
4. GL
5. NC
6. the rest
The idea was to found a second city by rush buying a settler after NC finishes.
I ran the tradition game first, which is a disadvantage , but i actually found more goodie huts anyway, and i got lucky and managed to steal another worker out of a barbarian camp at turn 60.
At turn 82 -
Beijing Pop 6
Shanghai Pop 1
Beakers per turn 28
Liberty/Tradition
Beijing Pop 7 (the granary effect)
Shanghai Pop 1
Beakers per turn 32 (bigger cap)
Tradition Timeline
T6 scout finished
T18 worker finished
T20 writing discovered, Liberty opener
T34 Legalism (free monument) enacted
T44 Monarchy (Extra gold and happiness)
T47 GL finished
T56 Aristocracy (15% wonder production bonus) enacted
T62 NC finished
T68 Shanghai founded
Liberty Timeline
T8 Monument finished
T14 Scout finished, start building Granary
T20 Writing researched
T22 Citizenship enacted (+25% tile improvement construction speed), receive free worker
T23 Granary finished, GL start
T48 GL finished (only one turn later despite starting 3 turns later, due to faster tile improvement gain in production and faster pop growth from having time to build granary)
T52 Legalism enacted
T60 NC finished
Not enough gold to buy a settler yet!
T69 Settler bought
T75 Shanghai founded
T77 Monarchy enacted
I don't know what this proves, other than there's not much in it either way, by turn 82.