Q:

Does Coffee Script allow using Javascript libraries? 

It looks like Google's Dart language doesn't allow you to call native js functions (say, using jQuery or my existing .js code). 
Does CoffeeScript allow any of the above? 

A:

yes you can use any javascript library with coffescript, just include the lib the usual way and write your code in the coffeescript 'style', so for a jquery example:
$(function () {
    $('.something').on('click', function () {
        console.log('you clicked me');
    });
});

becomes
$ ->
    $(".button").on "click", ->
        console.log('you clicked me');

A quick google found some ineresting blog's on the subject, coffeescript & jquery fun and using jquery with coffeescript. 
There is also a pragmantic programmer book with a chapter focused on using jquery and backbone in coffeescript applications
n.b.  as pointed out, remember that the coffeescript 'compiler' wont check that functions exist, only that the syntax is correct

A:

You can use jQuery and native JavaScript functions.  You simply need to write them in the correct CoffeeScript syntax. 
Bear in mind that CoffeeScript is a source to source compiler.  It will transpile CoffeeScript to JavaScript.  It won't know whether any specified functions exist. 
So if you wrote this CoffeeScript, it would compile just fine:
words = ["hello", "world"]
alert word.touppercase() for word in words

Note that touppercase() is undefined in JavaScript.  It should be toUpperCase().  Nonetheless, CoffeeScript will output:
var word, words, _i, _len;

words = ["hello", "world"];

for (_i = 0, _len = words.length; _i < _len; _i++) {
  word = words[_i];
  alert(word.touppercase());
}

You would then run into the error as a JavaScript error once you ran this in your browser, not a CoffeeScript error.  You can use the "Try CoffeeScript" link on CoffeeScript site to see how the translation takes place and try to run it.  You can also try it in jsFiddle by changing the Panels option to use CoffeeScript instead of JavaScript.