Although I don't believe that the entry list for the Daytona 500 has been released yet, picks can be submitted as soon as you feel comfortable with your choice. (I've received one already.)
And although the rules allow for changing your pick for a race up until the pick deadline, let's not get carried away with making a pick and then changing it numerous times.
Regarding the submittal of picks for future races (or even submitting picks on a weekly basis, for that matter), because I plan on being in the game this year, knowing the pick(s) of others in advance could possibly influence my pick.
If this is somehow an issue for some, you'll just have to trust me to not look at your pick until after I've made mine. My plan is to record picks during the middle of the week prior to the race, having made my pick before seeing what other picks have been submitted.
So having said all that, yes, you can submit driver picks for future races if that works for you.