I felt that Robert Kurzban presented a pretty good argument against the "willpower as a resource" model in Why Everyone (Else) Is a Hypocrite: [...] Elsewhere in the book (I forget where) he also notes that the easiest explanation for people to go low on willpower when hungry is simply that a situation where your body urgently needs food is a situation where your brain considers everything that’s not directly related to acquiring food to have a very high opportunity cost. It seems like a more elegant and realistic explanation than saying the common folk-psychological explanation that seems to suggest something like willpower being a resource that you lose when you’re hungry or tired. It’s more of a question of the evolutionary tradeoffs being different when you’re hungry or tired, which leads to different cognitive costs.

The standard metaphor is "willpower is like a muscle". This implies that by regularly exercising it, you can strengthen it, but also that if you use it too much in the short term, it can get tired quickly. So yes and yes.