To the extent my soil is 50% organic (split between compost and coir) I guess that qualifies it as containing organic fertilizer. I have gone for long periods without providing (synthetic) fertilizer, and the most obvious differences when I do provide additional nutrients have to do with growth and branching and especially flowering.
When you rely on the breakdown of organic material to provide all the nutrients your plants need, you have to take into account the limited lifespan of that material in soil. Different kinds of compost last different amounts of time, but the kind I use now breaks down pretty completely after about a year. It turns to dust and washes out and the soil level drops accordingly if there aren't enough roots sprouting to fill the space. So you can rely on compost for your nutrients, but you have to replace it every so often (by repotting) in order to compensate for the ongoing breakdown in the pot.
My use of (synthetic) nutrients has to do in part with my general laziness and refusal to repot most of my plants every year. I suppose you could make some kind of compost tea to serve the same purpose, and "organic fertilizer" could also go a lot of other directions. But my own experience is probably similar to most people's in that the compost in the soil serves the role of an organic fertilizer, while it lasts.
For what it's worth, any use of nutrients for cacti and succulents should be measured and limited, usually to much less than the manufacturer's general recommendation... I get all the activity I need out of 50 ppm N on a regular basis, which is a few fold lower than other plants enjoy and up to 20 times lower than you may find recommended on certain brands. Consistency of dosage is one big advantage of the bottled or boxed kind of nutrients.
