Importing your podcast will not affect your listeners as long as your podcast feed is correctly redirected.
When you redirect your feed from the old RSS URL to the new one, listening platforms such as Apple Podcasts and Spotify automatically update where they pull your show information from. Your podcast listing and subscribers stay the same.
Your existing RSS listening platforms stay the same once you complete the redirect to Riverside, even if Riverside does not have a direct integration with them. New episodes that you publish on Riverside appear on any platform that follows your RSS feed.