Yes it is possible the vaccine for FIV can show as a positive on a test result. Not sure of the stats on how often this happens though.
We call it feline AIDS because basically it is.
http://www.winnfelinehealth.org/health/FeLV-FIV.html
FIV belongs to the same family of viruses as HIV (human immunodeficiency virus) and immunodeficiency viruses in other species. This family of viruses (Lentiviruses) is known for being species-specific, for life-long infection, and for slowly progressive diseases. FIV is not transmissible from cats to people, and HIV is not transmissible to from people to cats.
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