Originally, pretty much any cosmetics or perfumes were extracted from naturally forming products. You want to have rosy cheeks? Rub the cut surface of a beet on your face. You want to smell like flowers? Rub flowers on yourself, or make a solution of flowers and water or alcohol to do the same. Want to have a pale foundation? Use a cream that includes lead (it reflects light, and therefore has a white color!), and then die prematurely of lead poisoning (it causes brain damage!) It is only in the past 150 years or so since the invention and development of industrial chemistry that we have been able to synthesize certain chemicals. Where before if you wanted a vanilla flavor, you had to go pick the flowers from a tropical isle and strip out the vanilla "beans." Now it is possible to manufacture things like vanilla in a factory. Similarly, it is now possible to synthesize many ingredients for things like cosmetics.
That said, the basic answer is "yes." There are plenty of ingredients that are far cheaper (and in some ways better) to get from organisms. The bright red color in many cosmetics that is called carmine is really a ground up bug. The heavy musky scent in many perfumes can be from glands found in deer, or from a byproduct of whale digestion. (Most of those last two are now replaced by synthetic substitutes, though.) And in any case, many synthetics are made using chemicals purified from plants and the like.
The next question would be, "How much?" As in, how much of all the cosmetics and perfume ingredients come from such sources? To be honest, I really don't know. My guess would be at this point that the minority of ingredients are from natural sources, and that most are synthetic, but that is just a hunch based on the economics of it.