Two weeks before (30-5-2013) I submitted Disavow request to Google and it was successfully submitted. Today I found some changes in my Google webmaster tool. I found that some of bad links has been removed which I mentioned in the Disavow request text file. I don't know whether it happened because of Google action. I found some of my links has been disappeared. But Matt Cutts said that "It can definitely take some time, and potentially months. There’s a time delay for data to be baked into the index. Then there can also be the time delay after that for data to be refreshed in various algorithms.". Then how those sites removed within two weeks? I even found that some links that i didn't mentioned in the Disavow file also removed. I didn't request Google to reconsider my site. Does a Google team member manually check the Disavow request file? Or another reasons for this change? Does anybody heard like this before?
Sadly, I wouldn't hold your breath. I guess there are a few random posts about people who have actually gotten their site out of a penalty, but most webmasters haven't found the tool a source of joy.
I believe disavow tool is not as helpful for removing the backlinks you mention, but it helps Google to find which sites are worth to be penalised. Really, it looks like Google is just collecting info about sites, and the most this site is mentioned in disavow tool as a bad one, the more are the chances it'll get penalised. Because, Myfreeforum mentioned it well 'webmasters haven't found the tool a source of joy'. There's no such person that will tell you for sure if it works and how much time it takes.. well, except Matt Cutts I think.
Most of what you hear about the disavow tool is unsubstantiated rumors and gossip. Very little is actually known making answering your question almost impossible.
This is an interesting article about disavow: http://moz.com/blog/google-disavow-tool I think it will answer your question. With regards to some links disappearing. The other day, I was checking the backlinks to a site I bought last year as it had a lot of links I would call spammy (footer ones). Mostly I had removed them, but still tens of thousands showing, so I was going to disavow them. Anyway, when I checked, they had all gone. On checking the sites (I had a note of some of the domain names), the links weren't on there, so they were removed as Google refreshed its link data. Did you check the pages where the links were supposed to be? Maybe they have been dropped due to the links no longer existing.