CVIs represent the veterinarian's word that the animal in question is free of any signs of disease, especially infectious disease, and that the animal is healthy enough to travel. If I were presented with a cat that was FIV+, and I knew it was FIV+, even if it was asymptomatic, then I would not be comfortable signing a CVI for that animal.
Now, do I feel that this cat would be unlikely to spread FIV under the care of a responsible owner? Yes, absolutely. Would I risk my license and accreditation by signing something that I knew was false on a federal document? Probably not. It wouldn't be anything against you or your cat, but falsifying information on a CVI is a big deal, and I'm a stickler. Ask me again in ten years, when I'm not a paranoid newbie vet, and you might get a different answer.
Now, if I did not know the cat's FIV/FeLV status, and the cat was asymptomatic and appeared healthy (i.e. if I had no reason to request FIV/FeLV testing and the cat had previously tested negative), then I would sign a CVI - but I wouldn't have any information about the cat other than my physical exam findings.
Airlines don't always check CVIs for transported animals, but if you are asked for one and can't produce it... rut roh.