Hello Kat, I guess the analogy would be "can a brain surgeon operate on a patient with only a limited knowledge of the brains anatomy?" I'm not a brain surgeon but I'm almost positive I could operate on the brain but I don't really know what the outcome would be, and I'm certain it would not end well!
However, anyone interested in Maya enough to learn some basics can use the program in a very short time. I wouldn't expect pixar quality end results but sure, students can learn a lot in a short time. For intro Maya stuff, it should be more about learning the core concepts of how to use the program, and then the color, design, and graphics elements come into the picture as a byproduct of learning about how to use Maya in all sorts of different ways.