Yes , it depends on the disease. For example, if a dog seems lethargic, a vet may take a full blood chem, and find out the dog is anaemic. This can be caused by several things - including AIHA - and in the time it takes a vet to find out what has caused it, a dog with AIHA can die as their red blood cell count can drop very dramatically. Like with Hamish, and IMTP, platelets can drop very fast and a dog can bleed out, internally, without the vet knowing what's wrong. One of my mother's dogs died from AIHA about 9 years ago, the first sign of her being ill was a collapse, she died the next day despite massive doses of steroids (correct treatment).
Back to the OP and OQ - a dog that is not entirely 100% healthy should not be vaccinated (according to the manufacturers recommendations) so I think that rules out Paddy.