Correct that Coffeescript is a Javascript generator. Also correct that source code can be clearer. There are absolutely no tricks that can be done in js that can't be done in Coffeescript -- you can drop into pure js if you need to -- and I'm not sure I've ever heard of anyone needing to do this. If you want to drop into Javascript, simply enclose the expression in backticks:
`var foo = 42`
I would disagree that the code is "bigger". I would assert that most extra bytes in the code are ones you should have been inserting anyhow but didn't -- like adding a namespace wrapper around your own code. In some cases, Coffeescript has clever helpers that factor out common usage patterns so they aren't coded one-off. You can figure out which these are by reading the generated js a bit.
In terms of advantages, I guess it depends a lot on how you think about code. I'm a fan of encapsulating a slab of functionality in a class and hate the Javascript prototype-based object definition. Coffeescript is more Rubyish or Pythonesque in terms of declaring classes and also in terms of inheritance.
My advice to you is: 1) Get Trevor Burnham's Coffeescript book and get a taste of how Coffeescript works in practice; 2) Cobble together a few simple examples that address your kind of use case; 3) See how you like it after you get comfortable with the syntax.
Note: The Coffeescript Google Group is a great resource and people answer questions quickly there -- it's likely someone has encountered whatever's puzzling you before and will share an answer. Trevor lists a complete set of resources in his book. (No, I don't get paid to give him props on the book :)