In looking for an answer, I found a lot of information about KSES and wp_kses_allowed_html, but that seems to be used to change all of the allowed tags. I did not find any documentation that described how the Aside post format behaves, other than the information that it is good for short post without titles.

I am using the Expound theme and it does not provide an option to set full or excerpt on category pages. The excerpt display is what it uses, and that format removes hyperlinks, etc..