In a word, "no".
The only handwriting fonts that you can reliably expect to be on most people's computers are the ones that nobody in their right mind would want to use - eg, Comic Sans and Lucida Handwriting. There is no high-quality handwriting font that has anywhere near widespread market penetration.
The options that you have depend on what it is needed for. If it is just for headings or very short inserts, you could use images or sIFR. If it is for one particular page, it might be better to get a really good font yourself and create that page as a PDF.
If it is for body text throughout the site, then my advice would be to do a Nancy Reagan. There is a good reason why most websites use only a very small number of fonts, and that is that there is only a very small number of fonts that are suitable for reading body text on screen at the font size typically found on websites. A handwriting font, even a really good one that is great for print, is unlikely to be good to read on screen - particularly without anti-aliasing or Cleartype (or similar).