Just a note on semantics: From what I've heard, the auratus in Hawaii are currently classified as an Introduced Species, rather than an Invasive Species. The former denoting a species that has established a local population, but is not known to spread to a degree believed to cause damage to the environment, human economy or human health. (wikipedia for exact definitions)
That being said, if you introduce them to a new island, it'll be extremely difficult to predict if that introduction will result in them turning invasive in that environment.
Separate from reality, I do get a laugh imagining a scenario where they are introduced and aid in the destruction of friggen cane toads by poisoning them upon consumption.