i've never tried that method. i've done it two ways now on emperor (this thread was different cuz its King and it was with Russia and it wasnt planned either, haha).
one was a Great Person strategy and using scientists to pop free techs and engineers to hurry wonders and using the free generals for golden ages. if i get the Temple of Artemis, which didnt happen every game, then i also get 100 gold for every GP popped which really added up over the length of a game.
Mausoleum of Helicarnassus...
Temple is good (+10% growth and 25% reduction in ranged unit cost), but it's steadily fallen down my priority list as I've got more of a handle on the Civ V versions of the Wonders. Mausoleum is probably the Wonder that rewards a specific strategy more than any other - with a GP-heavy focus you can be producing them every few turns, and 100 gold is a useful amount to gain for free at any point in the game.
the artists were used for culture tile improvements and merchants were either used for golden ages or trade missions with friendly CS's. (some games i had no friendly CS's.)
Merchants also increase influence with CSes (unless you're at war with them), so can make CSes friendly...
and choosing to finish policies in a particular order really helps. i have messed with which ones i go for and in what order so far and had different results. sometimes the game dictates what you need like picking a policy that gets your happiness out of trouble when you needed to pick another one for a long term bonus. regardless, Liberty, Piety, Freedom are required while the other two are up to you. I've done Lib/Piety/Free with Honor/Commerce and with Honor/Tradition. I've found that I think Commerce kind of sucks. doesnt boost gold nearly enough to be considered a commerce-specific tree, imo, and the naval bonuses are nicer for military aggression which i wasnt doing. the luxury happiness bonus in commerce was just less than the happiness bonus from Tradition.
Commerce has some useful stuff, but also some junk - mainly useful because the bonus for opening the policy branch is a big boost to gold output in the capital, which is important if your capital is gold-specialised. I get it most games.
As a side note, I feel there is a balance issue with Patronage (as someone who's exploited it). If you use CSes at all (as you should), the bonus you get for opening the policy tree (basically equivalent to giving you the Greek UA) is by far the most powerful of the opening policies in any branch. I think that should probably be the benefit you get for finishing rather than starting Patronage, since otherwise it's just much too easy to build up influence in increments of 250 gold every so often, knowing that you can wait for a long time and still gain a substantial advantage with your next cash injection. I played my last game as Greece, and it was practically impossible for the AI to break my hold on CSes other than by eliminating them through warfare.
and the 2nd method used Patronage/Tradition for the other 2 for the option of winning a UN vote. this was with 7 cities and 1 puppet. these were the benefits i saw from trying this:
1. you dont have to focus on science other than to keep up a military defense
Not really true. The UN requires you to have completed the majority of techs in three tech branches to unlock Globalization. Then you have the build time and the 10-turn wait. So unless you're relying on someone else building the UN (which they shouldn't if you have a diplomacy advantage) you need to tech fairly hard. I was ahead of my rivals by a long way in an Emperor game technologically recently, entering the Modern Era before the 20th Century, and I finally completed the UN in 1999 having started it as soon as I got Globalization.
2. CSs will gift you culture/tech/units and occasionally GPs (you have to be picky which ones you ally with based on what they can provide--lux's, units, etc.)
One thing I found was just how useful the science bonus from allied CSes is with that Patronage policy.
3. finishing the patronage tree makes it a little more difficult for other civs to win with a UN vote
4. you dont need to build the UN cuz another civ will do it for you (risky if none of them do it, i just havent been in a game when at least one of them didnt)
In my last game, had I not built it, no one else would have been close to the necessary tech level in time, and having denied Arabia and India all the city-states, both apparently gave up any designs on a diplomatic victory.