Short answer
Rarely. Alpacas have no upper front teeth, so a nip is more of a pinch. Intact males can inflict real damage with their fighting teeth, mostly on other males.
Alpacas graze with lower incisors against a hard upper dental pad, so a nibble from a female or gelding is mostly harmless.
Adult males develop sharp fighting teeth around 2-3 years of age and can wound other males' legs, ears and testicles. These are usually trimmed. A male that bites people is a warning sign of aberrant behavior.
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