I guess the dust of disappearance is a 1 charge use-activated item that cast the spell "improved invisibility". I would treat it as if a spell caster of the level of creator of the dust had cast "imporved invisibility" on the recipient.
Therefore, if the dispel works, the character turns visible.
If the character runs into an antimagic field, the magic is supressed until the invisible person runs out of it again.