How common is it to have internet fast enough that a POST request completes between characters? I would expect it's completion in a second or two, enough time for a human to type about 5-15 characters, making the timing information completely meaningless.
This would require that after a second or two the post requests will be instant, and after that second or two they will travel back in time to be delivered simultaneously with all the other requests.
The timing information, despite possibly arriving with a bit of a delay will be just fine. Not only that, but if they really wanted they could just grab the TCP timestamps.