A reputable shelter/rescue generally will NOT adopt out a cat with diseases to a home with current cats. In fact, yesterday when my brother was looking for a second cat, he had to turn away and was denied to adopt a very precious cream/orange colored kitten because she has some sort of disease and it's contagious.

I know there are a lot of people who don't bother to test for certain diseases and adopt them out to homes with other cats leaving them at risk. Personally, i'll never get any animal from a shelter/rescue that works out of their home.

In other words, it's never happened to me (although i've never adopted a cat myself, my friends/family always ask me to come along and help them choose pets to adopt.)