Whether your pup has immunity is determined by several factors .....
The number of vaccines given has
nothing to do with protection. In order for protection to be achieved, the vaccine must be given when it can penetrate maternal antibodies.....If the pup was closer to 6-8 weeks the chances of the vaccine producing antibodies is slim....If the pup was older, say 14-16 weeks then the chances of the vaccine producing antibodies is much better. The older the pup the better.....If the pup was 14 -16 weeks old when he received his first parvo or distemper then only one of each would have been sufficient not the three that we are accustomed to......They give three because they are giving them too young.....The answer is not to vaccinate earlier or more frequently, but to vaccinate scientifically.
Was the vaccines given separately or given too close together to each other?....The time between vaccines should be three weeks. It takes up to two weeks for immunity to form after a vaccination is given; it's not instantaneous. If another vaccine, even for a different virus, is given during the two week period following a vaccination, it can interfere with the immunity from the first vaccine as well as the second. Waiting a bare
minimum of two weeks between vaccinations is an immunological requirement.
Three is better.
Was the pup stressed at the time of the vaccine? Stress could include environmental extremes, as in a pup just arriving in it's new home, handling, inadequate nutrition, parasitism, and other diseases. While it is common for vets to vaccinate stressed animals, these animals are more susceptible to adverse vaccine reactions and frequently do not develop an adequate immune response. Immune stressed animals develop limited protection from vaccinations.
I know most vets never mention these things when administering vaccines but they are very important factors .....Vaccines should not be just administered willy-nilly by the vet, but sad to say this is more the norm these days.....Sorry so long but I just couldn't answer in a "yes" or "no" answer with out giving you more info to consider.....