No, not necessarily. As explained here, there are several ways to listen to the show that have nothing to do with iTunes.

However, the major advantage of iTunes is providing for easy podcast subscription. What's that? Podcasting is a word that refers to offering audio or video content (basically a show) over the internet in a thing called an RSS feed. So what? So, that means that a person who wants a show offered with podcasting technology can 'subscribe' to that show, meaning that as every new episode is released, it's automatically downloaded to the subscriber's computer for easy consumption. In other words, rather than placing the burden on you to come check the website for new content, that content is delivered to you. iTunes is the largest and possibly easiest podcast distributor.

Thus, if you go here, you can see a preview of the iTunes page for Pop Goes Catholicism, that lists the episodes currently available for download there. And if you have iTunes, here's what the PGC page looks like:

You can see that you can either download individual episodes by clicking the buttons under the Price column or simply click the Subscribe Free button and the latest episode will automatically begin downloading. (You can then go to the show in the Podcast section of your iTunes library and either download the rest or choose from those available. Afterward, new episodes will automatically download to your computer and show up under the show name in the Podcasts section of your iTunes window.)