Yes and no ;)
If you didn't disable the app lock screen widget in the settings, then the player notification will be displayed on your watch allowing you to play/pause and skip to the previous/next episode.
You will also have access to the new episodes as well as the downloaded episodes notifications if you didn't disable them in the app Settings.
So why did I say it didn't support wearables?
For now there's not dedicated part of the app that can be installed on the watch itself, allowing you for example to trigger the podcast update or start the playback with a voice command.