You most likely can. Just listening to people type on a keyboard gives a very unique feel with each person. Try it sometime, listen to family members and colleagues type or find some youtube video. I can ID all my family members and some coworkers by the sound of their typing.
Obviously, if you can get the content of what they're typing, it gets much easier still. I think I've seen papers where they ID programmers based on the code they've produced. This applies to other types of writing too.
The main problem here is that even if you could do it, why would you? There are over 3.4 billion Internet users in the world. Given that people share IP addresses and even browsers, what's the actually gain identifying someone through typeahead search keystroke jitter? This would spend a lot of effort, and and then tell you what that a cookie doesn't?
I can't imagine that it's actually worth the effort.
Obviously, if you can get the content of what they're typing, it gets much easier still. I think I've seen papers where they ID programmers based on the code they've produced. This applies to other types of writing too.
You can build a model from keystroke timings and figure out people's SSH passwords too. https://www.usenix.org/legacy/events/sec01/full_papers/song/...