Question

Do you mean:

1. Using Adobe Audition to create your podcast, or
2. Using Adobe Podcast (Beta)? https://podcast.adobe.com

Obviously you can... although finding out what Adobe have to say about this isn't so easy, even when I've given you the link to the source of it!  But in the past, Adobe have been reasonably consistent about what you can and can't do with their software, so it's unlikely that this will be any different. The jist of it is that as long as you don't abuse their actual software in any way, and just distribute your material, then you are free to do so.

Of course you don't have to take my word for this, and neither should you. With the caveat mentioned above, the actual legal terms of use are here. Have a look at the Software link, and note especially what it says in section 1.3.