The really basic answer is that it keeps the chronological order. So it doesn't automatically add the post at the end of the existing comment chain, or anything of that sort. Think of it as if it never were an answer, and was just posted as a comment the whole time. In this sense it could displace existing comments, since the converted answer might fit between the time two comments were posted, and make the conversation look strange.
The same thing happens to any comments on the answer when it is converted. They move along with the answer and similarly keep to the chronology. This is when converting answers gets messy, since it means there are two conversations happening in the one comment chain.
So if the answer is older than the existing comments, then it's last in the chronology and would thus appear last in the comment chain.