Farming bonuses do actually have an effect, but it.. doesn't work quite as you'd expect. The whole food/population/farm mechanic in general doesn't really make sense, I suspect it's just a placeholder until a final - more intuitive - system takes its place. I did a little experimenting, and here's how it works now:
City 1: I built a city next to a fertile land but didn't build a farm or do any research, and let it grow until population stagnated and food plummeted to the minimum amount. This left me with 115 population and 11 food. I built a farm, food increased, eventually surpassing population so that population could increase as well, which slowed down food growth and eventually caused food to decrease. The end result was 163 population and 15 food.
City 2: Still without doing any agriculture research, I built a city next to a fertile land and immediately built a farm. It hit about 174 population before stagnating. Note this is higher than city 1, so the timing of building the farm has an effect.
City 3: I researched 50x farming upgrades, then repeated example 1: built a city next to a fertile plot without building a farm -> let it hit maximum population -> built a farm. It hit 170 population in the end (7 higher than city 1 reached without farming upgrades).
City 4: Still with 50x farming upgrades, I repeated example 2: built a city next to a fertile plot and immediately built a farm, it grew to 183 population before stagnating (9 higher than city 2 reached without farming upgrades). Note that at this point, despite the 50x farming upgrades, cities 1 and 2 were still at 163 and 174 population.
City 5: I built a city nowhere near a fertile land, it reached 130-something population (the game crashed before I could write down the number). Note that this is higher than the 115 population that city 1 reached without a farm, so farming upgrades seem to help food generation/maximum population even in cities without farms.
*Building a farm immediately after building a city will wind you up with a higher maximum population than building a city and adding the farm later on..
*Farming upgrades help cities that are still growing and future cities reach higher populations, but do nothing for cities that have already stagnated.
Recommendation, just in case you folks at Stardock don't already have a better economic system in the works (which I'm sure you do): whether you build a farm sooner or later shouldn't affect your final, maximum population - building the farm sooner should just make the city grow faster and hit that maximum population sooner. Farming upgrades should affect all cities equally, regardless of whether the city has stagnated, is still growing, or has yet to be founded at the time you actually research the farming upgrade. How to accomplish this? The way food and population interact needs to be changed, it doesn't exactly make sense at the moment and the strangeness of farms and agricultural research is just a side effect of that food/population interaction.