With the bottom 10% of GMAT scores at UC Davis of 660, I would say that your 580 puts you pretty far outside what a typical applicant would look like. Not to say that it would be impossible to be accepted, since the GMAT is only one part of the application. Without knowing the rest of your profile it would be impossible to say you chances. All that being said, to give you a better answer to your questions, how were you "approached" by the admissions team? Did you just receive a marketing email? Or contacted directly by an admissions team member? The reason I ask, is many schools just market to individuals that send them scores, because they know that you are considering their school. Now if you havn't applied yet, they may be trying to push up applicants b/c they are short of what they expected this year, so they sent out an email blast. This doesn't mean that your chances of getting in are better b/c they like you or something, but it does mean that they havn't filled the class yet. If the rest of your application is strong, I might conside applying. If not, I might wait until the next years application season, retake the GMAT, or work very hard to improve other aspects of your profile. The next year of applications is just around the corner!
New to the GMAT Club? <START HERE>GMAT Club Premium Membership - big benefits and savings
My GMAT and BSchool Tips: