No! PHPExcel doesn't have any built-in logic to do this; and nor does any other library that I'm aware of.
You'd need to write some code yourself to handle the conversion from HTML to a Rich Text Run.... there's some logic inside the HTML Reader that you might be able to use as the basis for this.
EDIT
Since this answer was written, a helper class has been added to the PHPExcel library that will take a basic block of simple html markup and convert it to a rich text object that can be set as a cell value. This is the PHPExcel_Helper_HTML class, with it's toRichTextObject() method, that takes an argument of a block of html and returns a Rich Text Object. There are examples demonstrating its use in Examples/42richText.php
$html = '<font color="#0000ff">
<h1 align="center">My very first example of rich text<br />generated from html markup</h1>
<p>
<font size="14" COLOR="rgb(0,255,128)">
<b>This block</b> contains an <i>italicized</i> word;
while this block uses an <u>underline</u>.
</font>
</p>
<p align="right"><font size="9" color="red">
I want to eat <ins><del>healthy food</del> <strong>pizza</strong></ins>.
</font>
';
$wizard = new PHPExcel_Helper_HTML;
$richText = $wizard->toRichTextObject($html);
While not all markup is supported, and it doesn't use stylesheets, and only a limited set of inline style elements, it works well enough with basic markup elements.