What you are talking about is called "OCR", Optical Character Recognition. OneNote has had it for a couple of versions now.
The OCR in OneNote is rudimentary. It works best on typed characters. I don't know how well it will work with hand writing. But you can be sure there are likely to be many spelling errors in your conversion.
OCR anything with OneNote 2007 and 2010
http://www.howtogeek.com/howto/14595/ocr-anything-with-onenote-2007-and-2010/
Word 2013 also does some pseudo OCR, extracting text from PDFs, but I don't expect it to work with your handwritten PDFs.
If OneNote doesn't do a good job you should try some other OCR tools, including the MODI, MS Office Document Imaging which came with Office 2007 and earlier. You can still get free copies of it.
OCR - MS Document Imaging / Onenote 2010
Using Microsoft Office Document Imaging in Office 2010
http://www.brighthub.com/computing/windows-platform/articles/91749.aspx
2003 Office Document Imaging - Part 1 – Using MODI
http://news.office-watch.com/t/n.aspx?a=261
Helen Bradley looks at Office Document Scanning, which is a small dedicated interface for scanning documents.
2003 Office Document Imaging - Part 2
http://office-watch.com/t/n.aspx?a=262&z=0
17 August 2005 - Office Watch
We look at the faux printer that comes with Office 2003 plus the Document Imaging Tool that brings the scanning tool (mentioned in part 1) and the imaging writer together into a useful trio.
Adding MODI to Office 2007
http://answers.microsoft.com/en-us/office/forum/office\_2007-office\_install/installing-microsoft-document-image-writer-in/2d979d2a-3294-44dc-8cfa-6fedc7423669
Replace MODI in 2010
http://en.wikipedia.org/wiki/Microsoft_Office_Document_Imaging
If running Office 2010 which lacks MODI, here are a few alternatives (among others):
Extract Text from Images: 10 OCR Tools Compared (see the comments)
http://www.howtogeek.com/96712/extract-text-from-images-10-ocr-tool-compared/
How to extract
text from images: a comparison of 10 free OCR tools
http://www.freewaregenius.com/2011/11/01/how-to-extract-text-from-images-a-comparison-of-free-ocr-tools/