Even if you did that I think there are a lot of ways to identify you, using everything from your browsing patterns -- what sites, when and for how long -- to even just the account creation process itself; you'll still need to complete the captcha and with the "click all images that match" captchas that Google is currently using on reCAPTCHA (which btw was quite a bait-and-switch; they originally got a lot of people to use reCAPTCHA because the original purpose was to help book scanning, "read books, stop spam", remember?) as far as I've come to understand continuously sends your cursor position to Google servers, and with the movement data and the order and the timing that you press the images I would not be surprised if there was a pattern that uniquely identified you there.

Likewise websites that stream your input key by key instead of submitting the text when you press the submit button should in theory be able to easily identify you by the timing of your keypresses. I've only heard of a couple of instances of sending keys as-you-type but I think that if someone made the kind of project you spoke of above, then we would start seeing more tactics like the kinds I mention in order to counter that.

Even if you then proceed to disable JavaScript globally and only browse the web in 1.0 style with user-initiated GET and POST, the way that you write has some uniqueness to it that might be possible to identify.