You can't generate a podcast using WordPress/PowerPress and have the podcast posts not show up on the website. If you wanted to have your blog posts and podcast episodes separate so they don't appear in the same place, you could create special categories for each type of post and them link to those category archives using a menu or links from a static homepage. Alternatively, you could look into using post types but that can be complex and isn't something to be tried unless you're very comfortable with using post types already.
Another option would be to run the podcast from a separate WordPress installation, perhaps on a subdomain or subdirectory of the main site and then link to it from the main site.