My answer to this question used to be 'no'. However, I've found I've gradually gotten more productive early in the morning and super late at night. I'm not sure why as it's not really a preference for me - just how it's been working out.
I can only say that the best guitar riffs come up to me while in bed just before drifting into sleep, and I have the phone next to me to hum that fucker into it before I forget them or fall asleep having no chance of recalling anything the morning after.
How would you track this? Productivity itself seems subjective (is it just any output, completing hard tasks, creative flow, deep thinking…?) Depending on how I define it, I will have a different response.