Yes, Yorkies were originally bred as ratters. They would take them to the coal mines and put them in tunnels and have them catch rats. Also, there were used in a betting contest, where rats were in a pen and people would bet on how long it would take the terrier to kill the rats. Huddersfield Ben, said to be the foundation sire of the breed was reported to be very good at ratting contests.
Huddersfield Ben - Wikipedia, the free encyclopedia
To answer your question, I do not think this means that they are less susceptible to disease, only that small animals excite them and bring out the hunting instinct. I wouldn’t let Joey around a rat, if I had the choice.