Its been a while since I used Greasemonkey. If I understand you correctly you want to allow people to make "notes" on profile pages, but store the texton the individuals computer rather then in the database? Last time I used Greasemonkey there was no supported way to have local storage. There were some ways around this, like running a separate server to store stuff, or attempting to access some of the browser specific local storage so that was always a hassle to support.
It looks like you might be able to use the new HTML LocalStorage cookie type thing, but I've not tried it.
