No, it’s just your games, images and videos that can be saved onto an external Nintendo Switch memory card. Save files are all kept on internal storage – partially to prevent piracy – though thankfully they don’t take up too much room by themselves.
If you have a subscription to Nintendo Switch Online, you can also back up your save files to the cloud, though not all games are compatible with this feature. If you manage to break your console, you can restore your progress safely. You’re able to re-download any purchased game software for free too.