To the OP, if you have something decent on your resume, absolutely send it along. It shows that you're serious about what you're asking for. The worst case scenario is that they don't care about your resume - if that is true, they just won't read it.
To the posters saying undergrads shouldn't/don't typically have resumes, I have to disagree. You should be maintaining a resume during your undergraduate years with your education, work, and volunteer experience on it. There are two reasons for this: it saves you from having to come up with one on the spot when you graduate, and it is really useful to have some information about yourself available for situations like the one the OP is referring to. And you'll need one for many of the jobs you might apply for during school, as well.