A straightforward but imperfect way of knowing if there was an intent to style an element would be to check if the style
attribute of the element has a value or if the class
attribute of the element has been set.
http://jsfiddle.net/YbSpc/
HTML
<div id="test_unstyled"></div>
<div id="test_styled" style="background-color: red;" class="something"></div>
JS
var unstyled = document.getElementById('test_unstyled'),
styled = document.getElementById('test_styled');
console.log('test_unstyled is styled?', !!(unstyled.getAttribute('style') || unstyled.className));
console.log('test_styled is styled?', !!(styled.getAttribute('style') || styled.className));
However, this solution will not detect any styles applied through CSS selectors. If you want to take these in account, you will probably have to find out all the default styles applied by browsers and check against that, but this will get very hard to maintain and I don't recommend trying to implement this approach unless you are willing to develop and maintain a library for that sole purpose.
If you are publishing a plugin that others might use, it would probably be easier to implement an API
that would allow the plugin's client to decided wether they want the plugin styles to be applied or not.
You could also always include your stylesheet and users will be able to override the styles by loading their custom stylesheet.