I do not know the exact answer, but I'm pretty sure you won't have a problem going from one desktop to another. I do not believe the information is stored as a cookie - it would be a miniscule file, and I'm sure those notes are stored on the server.
Btw, I copy my analysis and paste it directly to Notes. I don't bother to space it out, since it isn't that hard to read anyway.
I've been using the Notes to write a lot of analysis. (This is unusual for me but I am especially motivated by one particular game.) I seem to notice they don't always store properly. Partly it is because I am on a PalmOS tablet sometimes, and the 'save note' button just doesn't work I think. But also I am wondering if I have a desktop and a laptop with Firefox and the javascript works OK, and I write a note on one of them to say xxx yyy, and then I go and edit it on another computer to say xxx yyy zzz, is there any chance the first computer would fail to pick up the change? This could happen if caching got in the way or if the note is stored in cookies. Also I would like to know the maximum possible length, since I am worried about possibly losing information if my analysis gets to be too long. I would be somewhat sad if I lost what I wrote! Thank you!