Under the iPad's operating system, iOS, one app does not have access to another app's file space. So such a filebrowser could never be written for a non-jail broken iPad because it could not see another app's filespace.
Apps can indirectly open files that are held in another app's filespace though. An app can register its ability with iOS to process a certain type of file format and then another app, using the 'Open in' or 'Open With' facility in iOS can 'offer' a file, sitting in its own file space, to another app - via iOS - to be opened in an app or apps that have registered their ability to process that type of file.
This is how the app GoodReader works. It basically tells iOS that it can, more or less, process any type or format of file (even if it can't). It can then import that format of file from an email attachment or similar source. Once it has the file, it can then determine whether it really is able to process it - for example PDFs, .doc, .zip etc. Those it can't it simply files waiting for an app to be available that can process it and has registered its ability to do this with iOS. Then, when you select that format file, you'll get the offer to open it in a compatible app.
But I digress....

- I'm afraid that GoodReader is the closest you'll get but no app can directly read another app's filespace....
Tim