No — Podpage hosts your website and displays the episodes from your RSS feed, but it does not host the feed itself. Your feed comes from your podcast host, which stores your audio files and publishes them for apps like Apple Podcasts and Spotify.
Podpage works with any podcast host with a valid RSS feed. If you're still choosing one, The Podcast Host's guide to podcast hosting is a good place to compare options.
For more on how hosting and Podpage fit together, see Can I upload episodes to Podpage?