Do departments usually have an area preference even though they post an open area ad? How reasonable is it to assume that they will be looking for someone in an area that is not currently represented strongly in their department?
The short answer: it varies. Sometimes you can infer what sorts of candidates an "open area" ad is targeted at based on information about the teaching duties or research. For larger institutions, they may well be simply seeking to bolster their department with an up and coming star. For smaller institutions, however, they may well seek nearly any solid candidate who's able to teach a wide variety of service courses. To succeed with open area ads, especially outside of R1 positions, I recommend assessing whether you could teach intro psych, methods, and statistics. If you can do well with all of those, emphasize it. I suspect you'll find greater odds of success.
I concur with DocJ. I'm in a small department and while it would be great to find someone to cover areas that none of our existing specialties cover… we're actually more interested in finding a great teacher and a colleague… and someone to help us spread out the load for multi-sectioned core courses such as: intro psych, methods, and statistics. So yes, def emphasize willingess and/or expertise to be able to cover these courses in addition to your subfield-specific course(s).