No. The main goal of Blubrry is to help you distribute your podcast content to podcasting devices, we're not in the business of being a web destination like YouTube or SoundCloud.
Anything that is synced to podcast enabled devices will not have this capability. Only a service that has their own infrastructure (as a destination) could do something like that. In other words, services that do not podcast the content but instead host it on their own web site (YouTube for video or SoundCloud for audio) can provide such functionality without concerns of end user privacy.
A company years ago tried to track usage in iTunes, it had a lot of push back from the community with it's "calling home to mamma" iTunes plugin. Difference here is that with the iTunes desktop application, one expects a level of privacy on what they are doing, where-as web based tracking it's an accepted practice to monitor what everyone is doing without fear of privacy concerns.