I don’t think he would have (or did) because, knowing all things and being completely filled with the Spirit, he would not need any external reminders. It is literally impossible (both now, and when he was on earth) for Jesus to forget any obligation that he has. (And he does have obligations — that is, things he needs to get done — but they are only the arrangements he freely enters into, which are founded in the promises he has made in the Scriptures.)
But, I’ve never thought that “what would Jesus do” is necessarily the best question. It is a helpful question. But since we are not Jesus (for example, we are not omniscient), the more precise question is “what would Jesus have me do?”
And I think he would say this about to-do lists: “If you can keep all your commitments and get done what you are called to do without writing anything down, no problem. But if you have more to do than your memory is able to hold, one of the other reasons I’ve given you a mind is so that you can figure out a better way to keep track of everything than just keeping it in your head. So go, do what you need to do to remember what you need to remember in order to get done what you need to get done.”
Something like that.