Is it possible to graduate without taking online classes?
Yes (based on your major), but I don’t see why you wouldn’t want to take one or two. A few classes have such large enrollments that it’s simply easier to take the classes online (and then go to the TA break out sessions). It’s typical to take 2 or 3, almost all in your first 2 years (before you start taking classes in your major).
In fact, some classes work better as online classes.