It can work, it all depends on how "specific" your site's CSS is. For example, if you have something like ".center .content h2" TinyMCE has no structure like that, so the h2 elements won't get the same styling.
The CSS file to use is set in the System Settings, using the editor_css_path setting.
What I usually have to do is use Firebug to view the actual Manager page and see the HTML that TinyMCE is using, then basically duplicate the relevant parts of the site CSS file with the addition of the TinyMCE classnames.
TinyMCE loads an iframe with this as the main editing field:
<body id="tinymce" class="mceContentBody" ...
So the CSS would use something like ".mceContentBody h2" instead of ".center .content h2".
Here's the HTML that TinyMCE inserts into a content field with just "hello" entered - everything in the <span>...</span> is TinyMCE:
<div id="x-form-el-ta" class="x-form-element" style="padding-left:105px">
<textarea id="ta" class="x-form-textarea x-form-field" name="ta" autocomplete="off" style="width: 791px; height: 396px; display: none;" aria-hidden="true"><p>Hello</p></textarea>
<span id="ta_parent" class="mceEditor cirkuitSkin" role="application" aria-labelledby="ta_voice">
<span id="ta_voice" class="mceVoiceLabel" style="display:none;">Rich Text Area</span>
<table id="ta_tbl" class="mceLayout" cellspacing="0" cellpadding="0" role="presentation" style="width: 95%; height: 400px;">
<tbody>
<tr class="mceFirst" role="presentation">
<tr>
<td class="mceIframeContainer mceFirst mceLast">
<iframe id="ta_ifr" frameborder="0" src="javascript:""" allowtransparency="true" title="Rich Text AreaPress ALT-F10 for toolbar. Press ALT-0 for help" style="width: 100%; height: 333px; display: block;">
<!DOCTYPE >
<html>
<head xmlns="http://www.w3.org/1999/xhtml">
<body id="tinymce" class="mceContentBody " contenteditable="true" onload="window.parent.tinyMCE.get('ta').onLoad.dispatch();" spellcheck="false" dir="ltr">
<p>
Hello
<br data-mce-bogus="1">
</p>
</body>
</html>
</iframe>
</td>
</tr>
<tr class="mceLast">
</tbody>
</table>
</span>
</div>
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