In all of past experiences once it's deleted it's gone forever. If you have emails that download to your computer, there might be a chance of recovery - but the chances are about 50/50.
What Happens When An Email Is Permanently Deleted From An AOL Or Yahoo Account? Can It Be Restored Somehow? Does It Remain On The Computer's Hard Drive?
Anything you delete is kept on FREE SPACE on your computer until they are over written by something else, especially e mails. I advise running a free cleaner (free space cleaner) such as CCleaner which now gives you the option to wipe FREE SPACE. This deletes anything you have deleted such as e mails, recycle bin etc....lets just say....personal stuff you don't want tracked too!... Do a google search for ccleaner...ITS FREE!