1script - 5:05 pm on Feb 24, 2012 (gmt 0)
All it can do is speed up the process and they may offer you some helpful advice as to what exactly it is they have become disgruntled about. This can at least put you in the right direction.
Helpful advise? From Google? Are you serious? Best I was ever able to get from them was: "we see improvements but one or more pages of your site still violate ..." I guess you can take it as a good news that they're still talking to you but that' about as helpful as they'll ever get.
Google is not going to help you rank better in Google. If they did, all they'd accomplish would be more workload for them because then another webmaster, the one who's pages you pushed back to Page 2, would submit his/her own recon request. And the cycle would just go on forever.