Are files saved to iCloud via 3rd party applications accessible from icloud.com web interface through browser?
You cannot access individual files on iCloud other than the ones made with the iWork suite and that are available on the iWork section of the icloud.com website.

When introducing iCloud, Steve Jobs mentioned that Apple did not think of this service as a big folder in the cloud--a direct contrast with Dropbox. I wrote about this before the launch of iCloud on this Ask Different answer. In short, iCloud is meant to be app-centric. 

I would not be surprised if the iWork section of the icloud.com website went away once native iCloud support is added to Keynote, Numbers and Pages. Like it or not, this makes business sense, as it encourages app purchasing. 

Hope this helps.