I don't see a problem with it, but like said above it is probably hit or miss with them, of course one food they love is mango.
In case anyone is curious
Carambola, also known as starfruit, is the fruit of Averrhoa carambola, a species of tree native to the Philippines, Indonesia, Malaysia, India, Bangladesh, and Sri Lanka. The fruit is a popular food throughout Southeast Asia, the South Pacific and parts of East Asia. The tree is also cultivated throughout non-indigenous tropical areas, such as in Costa Rica, Peru, Colombia, Jamaica, Trinidad, Ecuador, Guyana, Dominican Republic, Puerto Rico, Haiti, and Brazil, and, in the United States, in south Florida and Hawaii.
The fruit has ridges running down its sides (usually five); in cross-section, it resembles a star, hence its name. The number of ridges can vary from three to six or seven