I've seen very few dough recipes that would be impossible to convert from one method to another. Well, no-knead would be a little silly in the bowl of your food processor, but otherwise it's just a matter of changing a few things to convert from one style of kneading to the other.
Generally, the things that need to be changed are the amount of time you need to knead and the order you add ingredients.
But here's the thing about timing: in my opinion, any recipe that tells you to knead for a specific amount of time but doesn't give you any visual cues isn't a good recipe. There are too many variables that affect the gluten development, so time is not the best indicator. Sure, you can give a rough estimate so someone knows if they'll be kneading for 30 seconds or 20 minutes, but precise timing is impossible if you're using someone else's recipe.
Yes, there are exceptions to my "it's a bad recipe" rule. Not many. Kneading early in the process may be all about mixing and less about gluten development, so watching the clock is fine. But instructions to knead for 10 minutes before shaping a loaf is much less useful.
So, if you're relying on visual cues to tell you whether the kneading is done, converting from one kneading method to another means that you can rely on your senses rather than the clock. It's helpful to have an idea of when to check the dough, and that's most important with the food processor, since it's so much faster.
My rule of thumb with any dough in the food processor is to stop and check the dough shortly after it forms a ball. At that point, I check the gluten development and make sure there aren't any bits of dry ingredients or wet dough that need to be incorporated into the main dough ball. Sometimes there will be dry flour or a bit of wet goop just under the blade or bits of stray dough too high for the dough ball to reach, so I gather those up.
Then I continue processing in short bursts, maybe 15-30 seconds each, checking the dough each time to see if the gluten has developed fully and to let the dough rest and cool if it has become too warm.
When it comes to adding ingredients, the food processor makes it easy. Generally you start with all of the flour and similar dry ingredients (along with butter or oil, if you're using it) in the food processor bowl, including the yeast, if you're using instant yeast. If you're using active dry yeast, it's common to proof it in just a small amount of the water - about 1/4 cup.
The processor is first pulsed a few times to mix the dry ingredients and break up the bits of butter or oil. Then the liquids are added. With the exception of the proofed yeast in warm water, all of the liquids should be cold when they are added, to help keep the dough temperature down.
If you're proofed yeast in warm water, that goes in first, followed by the rest of the water or other liquids. All of the liquids should be added while the food processor is running, and as fast as the flour can absorb them. You don't want to add the liquid all at once, or you'll end up with a sloppy, sloshy mess that will take a long time to incorporate. When the dough begins to form a ball, it has enough moisture. Depending on the recipe, you can add more liquid, as needed.
Using a food processor is fast and efficient, and it makes kneading completely effortless. It also requires fewer steps, since all of the wet ingredients are added to all of the dry ingredients, so there's no need to think about adding items separately.
Since the processor is so efficient at kneading and so powerful, there's no concern about salt toughening the dough and making it harder to knead, or oil coating the strands of gluten - it powers through everything without hesitation and creates a smooth, silky, elastic dough.
That speed and power also makes the food processor very abusive to any add-ins. Chunks of cheese can become shreds in no time, and even seeds and nuts can take a beating. These need to be added to food processor recipes at the very end, and gently pulsed to combine, or they should be kneaded in by hand.
The speed and efficiency of the food processor also makes it a little bit harder to adjust recipes, so it's best to work with a tested formula. Once that ball of dough is formed, kneading is very close to being done. Trying to add more liquid or flour to correct the hydration at that point can lead to overheating or even overkneading the dough.