No they do not process quicker if the application is for travel sooner, the processing time on the website is an estimate for majority of files, you could be quicker or could be longer no one can say for sure. Also no one can say for sure if you will be approved or not.
Was the conference being paid by your employer or by the people hosting the conference? That would improve chances. Also if you get approved after the conference is over be prepared to come up with a new purpose of travel. Why would you want to come after your conference?