Hello,  With the Android, you get the option "Redirect Drives" this should do exactly what you're asking for.  It doesn't look like the iPad has that feature yet though.
Hi all,  I've searched through the user and admin guides, but can't find the answer I'm looking for.  Using the Windows client, you can choose (when browsing for files) to browse the local client hard disk that has been mapped through, or optionally use the \\tsclient reference.  What I'm wondering, is there the option to browse an IOS or Android device (assuming you're connecting with one of those devices) for files, like you can with the Windows client?
File Transfer from IOS/Android Devices?