Can you inspect a webapp's filesystem from the chrome dev tools?

I am working on a website that is using HTML5's Filesystem API to write some files to a temporary file system. Is there any way I can use the Chrome Developer tools to inspect the files I have written?

How do I view JavaScript files in Developer Tools?

You can also press Ctrl + Shift + C on your keyboard to open the developer tools. In the top-left section of the developer tools, make sure Elements (A) is selected at the top. In the condensed code under the Elements header, find the <script> tag containing a link to a . js file (B).

If you go to chrome://flags and enable "Enable Developer Tools experiments", then go to the Experiments tab in the Dev Tools settings, there's one named "FileSystem Inspection" that might work. I haven't tried it, though.