I am wondering if it is possible to post to the wall of the Facebook app page created for using Facebook in iOS. Rather than use the user login to post to their own wall, I
Yes, it's possible. From http://developers.facebook.com/docs/reference/api/application/:
To perform the following operations as an Application Page, and not the current user, you must use the Application's Page access token, not the user access token commonly used for modifying Graph API objects nor the Application access token. This access token can be retrieved by issuing an HTTP GET to /USER_ID/accounts with the manage_pages permission. This will return a list of Pages (including Application profile pages) to which the user has administrative access, along with an access_token for each Page.
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You can create a link, post or status message by issuing an HTTP POST request to the APP_ID/feed connection. To see more details please see links, posts, and status messages documentation.
To impersonate the Application when posting to the wall (i.e. post as the Application, and not the current user), you must use an Application Page access_token with the manage_pages and publish_stream permissions, as described under Application Access Tokens above.
So you first have to ask the API for an Application Page access token and then use this access token to post on the wall. The Facebook iOS SDK helps to construct the Graph API calls mentioned in the documentation cited above.