I would assume you must first be skilled at drawing before moving on to modeling and animation. Unfortunately, my art sucks. I attached a file showing how bad it is. I can see the world I have created in my head clear as day but I can't put it on paper. I assume I need technical knowledge on drawing, such as anatomy. I can only imagine how naive I seem in regards to the subject.

So I'm not a superb artist by any means, and most of what I do is more hobbyist than professional, but I would say that drawing is not a prerequisite to being able to do 3d modeling. I feel very similar to how you feel, that it's much tougher for me to put my creation on paper but I can visualize it very well in my head. I have found it easier to model than I have to draw.

Drawing is very helpful, and it can also be equally helpful to plan out a model as well (concept art), as tempting as it can be to just start. It can be sometimes better to have a crap drawing to reference from, or any sort of picture really, than nothing at all.

I would assume you must first be skilled at drawing before moving on to modeling and animation.

Any of the visual arts will help improve the others, this is because it improves your artistic eye. However each visual arts skill stands on it's own, so it uses techniques that the otter skills don't. As an example to learn drawing you need to learn how to hold your pencil or pen and for 3D modeling you need to learn your shortcuts.

Any one of the visual arts takes years to learn, you are considered a beginner when you finished school on your art or spend 3-4 years learning.

3D animation and 3D modeling isn't the same thing.

As a 3D modeler I spend a lot of time with animators and they know only the basics of 3d modeling, they will say the reverse for me.

As a 3D modeler clients expect me to also know animations, I am learning animations and am not even considered to be a beginner after two years of learning.

2D animation and 3D animation, isn't the same thing in the way that painting and digital painting isn't the same thing. Basically a person from one can easily learn the other, they only need to learn the technique.

All visual arts follow a similar principal of refinement, that is you start with a rough drawing and improve on it until you are happy with it.

The more you work with art the more you will notice what shapes and form objects are made from.

The principals of art apply to 2D and 3D, traditional and digital so any thing you can learn about any art is useful.

When some one says you need to know how to draw something to model it, they mean you need to know how to model something to draw it.

In other words you need to understand all shapes and forms and as much as possible about the object, so that you can remake it in your art form. There is no need to learn to draw if you want to make a 3D model.

This pretty much sums it up. If you know how to draw, the skills can certainly translate over to modeling, but it's not absolutely necessary to have that skill.