The tray icon is able to carry out the "update feeds", "download all new episodes" actions. You can configure gPodder to update the feeds every X minutes and also additionally configure it to download new episodes after an automatic update (when minimized).

The "minimized" status detection and the hiding from the task list doesn't work at the moment (so "hide to systray" doesn't work the way it does on the Desktop version), but once this is fixed, I think this is possible What I would also like to do is replace the pynotify notifications (from the Desktop version) with the corresponding upper-right-corner Maemo/Hildon notifications, so the user knows when new episodes are available, etc..

The "automatic podcast update" is already available in the "extras" tab of the preferences dialog, you just have to enable and configure them.

The "automatically download new episodes" option is currently global, but could be made per-podcast, if need be.