What are some specific benefits of having my name as a coauthor on a research paper as an undergrad?
Could this help me get into a better grad school (rather-- master's
  program) than I would otherwise be able to (pretty average GPA, to be
  honest)? Help secure some funding? etc


Yes, it can help you with all those things and more (including non-academia-related things like applying for a job in industry). Generally speaking, being a coauthor of a published paper in mathematics says good things about you and your math/STEM/academic/research abilities in any context in which someone would care about those abilities.

However, it's important to take things in perspective and understand that "just" the fact of your being a coauthor on a single paper will not make a huge difference in and of itself. E.g., a grad school or fellowship candidate with no publications can easily "beat" a candidate who has a publication if the former has other good things going for them (a better GPA, better recommendations etc) that the latter doesn't. What I would say matters a lot more is not just being a coauthor, but what you actually did to deserve being a coauthor. If you do an unusually good job on the project, this can translate to excellent recommendations, which will carry a far greater weight in a grad school application than the mere coauthorship line on your CV. If you were just a code monkey who did low quality work, the coauthorship would still be of some value but would overall not be worth very much.

Finally, I should mention that you seem to think that work that's "pretty purely computational" is less important or creative than other sorts of math research, but that is not universally true (although it may be true in specific instances). Even in a computational project there may still be a lot of room for creativity, and a chance to excel in all kinds of unexpected ways. Who knows, you may end up having an idea for a cool optimization that would extend the computational range of the algorithm enough to enable you to discover an amazing new phenomenon your collaborators did not even suspect existed (such things have happened many times). Besides, understanding complicated mathematical constructions well enough to translate them into code can be a highly nontrivial challenge. You would also get to experience the thrill of doing mathematical research and taking a part in the discovery of new knowledge, learn about working collaboratively with others, and probably derive many other benefits from the experience. So, to summarize, I would not scoff at the opportunity to take part in such a project. Doing it just for the paper coauthorship would probably be a bad idea, but doing it for the experience and knowledge you will gain, plus the chance of a coauthorship, seem like excellent reasons to me.