Can this cake be baked the day before when it is humid?

It's not a discrete crust, certainly nothing that's noticeably crunchy. The sugar adds a slight texture more than anything; I don't measure the sugar that I sprinkle on the pan but it's probably about 1.5 tablespoons. You should be fine.

It tastes better the next day. I am not surprised that Alice Waters called this her favorite cake: it's wonderful in its simplicity.