The answer to your question is "Yes!" Such a program now exists.
I have been involved in a project to do exactly what you described and would be happy to help you. Where other software requires you to hand enter your listings, this one does not. It works directly with your your database to create the appropriate XML feeds for direct posting to syndication services such as Trulia, Google and Others. The Bottom Line being that the feed several hundred listings could be created in a matter of seconds. Please see the link below for more info.
Becky, I just wanted to point out that Postlets (love love Postlets!) does NOT automatically syndicate to Craigslist. You have to use the "copy and paste" HTML text you referred to and actually go into Craigslist to create a post with the same flyer. The HTML text does make it super easy, though!