Your boy will be fine. He's only in slightly more danger (vaccinations do not prevent 100%) if the other dog is ill.
The danger from unvaccinated dogs is that these dogs can catch diseases, so the diseases become more widespread. Health authorities in the UK, have expressed a similar concern about childhood diseases, whcih were once killers, becoming more common, because of the trend in not having babies jabbed, due to worries over the ill effect of vaccines. They say that a child is in more danger of the ill effects of a disease becoming more common than from side effects of inoculation.
Barbara, Monty, Joly and Teddy.