Seriously Simple Podcasting does not make any changes to your site's templates. The only visual element that it adds is the podcast audio player and episode meta data if you select that option. The actual display and styling of the episodes, series and archives, however is governed by your theme. With that in mind it is possible to add templates to your theme that will control your podcast display.
By default our podcast archive URL is http://example.com/podcast and your RSS feed URL is http://example.com/feed/podcast, but you can change these by adding these snippets to your theme.
By adding a couple of quick snippets to your site you can hide the episode audio player or make any changes that you like to the episode details that are displayed beneath it by default.