metabolism - Do plants need O₂ to consume energy they've stored via sugar?

This question came up as I work my way through the answers to another question I just asked.

My understanding is that plant photosynthesis looks something like this (though with lots more going on under the hood):

$$\ce{6 CO_2 + 6H_2O + light -> C_6 H_{12} O_6 (sugar) + 6 O_2}$$

(source) and that the primary functions of the sugar are to store and transport energy. If that's true, then there's something fishy about the familiar view that plants need CO₂ to breathe and produce O₂, while animals need O₂ and produce CO₂. Doesn't a plant need just as much O₂ as an animal would when it (the plant) gets around to consuming the sugar it has produced? Doesn't consumption of the sugar take you back to the original reactants?