There is an excellent question at WebmasterWorld asking how does one know when Google does process your disavow link file?
The answer is not an easy one.
The only way now to really know is if you have a manual link penalty and you use the disavow file method to remove links and use no other methods for link removal. Then you submit a reconsideration request and Google responds that the request was satisfied - you can be safe to assume Google processed the disavow file successfully.
Another way is if you see your rankings shift significantly a week or so after the file is uploaded.
Right now, when you upload the file, Google doesn't tell you if they processed it. It would be nice to see a status of your disavow file from Google in Google Webmaster Tools but that feature is something not available yet.
Maybe in 2014?
Forum discussion at WebmasterWorld.