That is really an individual question. I have friends who have done it. My sister and brother-in-law like to leave in the evening and drive all night while the kids sleep for every trip they've ever taken. My husband and I cannot do it. Our first trip, we left at 3:45am hoping we could drive early morning and get there around midnight. We couldn't even make it to Seguin before someone had to pee. We hit Pensacola around dinner time, ate, and drove another hour before we were both tapped out. We found a Best Western in Mariana, Florida. I know people do it, but for us, it's a no go. I think having 3 drivers would make it easier.
By the way, if you leave early enough on a weekday, you can catch the brewery tour in Shiner at 10am (if you are in to that) and be in New Orleans by dinner.