Yes most top producers have staff to weed out the chaff and create a shortlist usually a dozen or so potential songs for each song to be recorded. The ten second rule normally applies...if the first ten seconds do not grab you then move on....that is what I believe most do when sifting through songs....I can usually spot a goodun or a badun within that time frame....or listeneing to a few selected seconds from the middle of the song is another option to create a shortlist. I was led to believe that staff writers if writing for an artist are given a brief as to what sort of subject matter and tempo etc a specific artist wants and they tend to write to measure.
However nothing is written in stone and each has his own way of working.....they may have staff or they may use songpluggers or they may ask around.....hell there is enough songs to choose from whichever way they do it.....
what surprises me is that despite having such a huge choice of really good songs out there...they still mostly pick crap.

http://www.soundclick.com/bands/songInfo.cfm?bandID=687727&songID=5238055