"Can this process produce the chiral asymmetry of these compounds that we see in biology?"
No, but if you imagine a primordial "soup" of complex carbon compounds produced by any or all of a variety of mechanisms, the first self replicating compound to appear might well introduce chirality by means of selective "consumption" of specific isomers. Of course, we're a long way from knowing what self replicating molecules might be involved, how life arose or even if self-replicating molecules were a step in the process..