I've got it working with an iPad app called FeedHopper, but the experience isn't ideal: it isn't obvious how to add a lesson feed and the embedded files attached to the lesson are listed as separate items rather than additions to the main lesson. There is no obvious sign that mp3 players are attached to the lessons -- you just have to know - and when you play them there is no support for embedded id3 tags, so you can't see the transcript while listening to the show as with the regular iTunes player.

http://itunes.apple.com/us/app/feedhopper-rss-reader/id361881998?mt=8

I'd be curious if someone knows a better app for this, comparable to DoubleTwist on Android.

Still, it's possible to manually provide the RSS feed and have it manage the download. The other big limitation is having no way to automatically download all of the related media for a particular feed, so it feels less useful as an organizational tool than just logging into the site with Safari.