The Angel will not ever get sick from eating Candy - in fact, eating candy is encouraged to keep its Angel Power up.
The only negative side effect from Candy is bats. If you don't manage to scare them off when you see them, they're more likely to show up when your Angel is eating, making your Angel very unhappy.
The main function of Angel Power is to determine what teen, adult, or special adult you get. Each character also has a maximum for how much AP they can have (for example, Marutchi Angel's highest possible AP is 50).
Angel Character Guide(BTW, the only time I've ever seen an Angel sick is after turning the light off and then on again.)
~OM21
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