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I can offer one data point: I run a browser-based LaTeX editor (http://www.writelatex.com) and currently 2% of visits come from iPads. 6% come from a mobile device of any kind. I'm not sure how many of those actually try to do any serious writing, though.

While the filesystem is not directly accessible by either users or apps for security reasons, it is possible for apps to communicate and/or exchange files. Your app can register the ability to open certain filetypes with the OS (e.g., so users can open mail attachments or Dropbox files in your app) and it can communicate directly with another app through custom URL schemes (e.g., to accomplish single-sign-on using the Facebook app).

I installed TeX writer in my iPad (the other iPad TeX version referenced around here in the comments), just for fun (when I needed to do some TeX on the go, I just ssh'd and looked at the PDF in Dropbox.) Finishing my PhD, I don't generate any more images, they are all already done. And TeX Writer is surprisingly effective as a compiler (feels faster than my desktop!) Love it as a proof of concept... but only use it sparingly. I don't think I'd use TeXPad any much, although the editor looks fancier