In theory, yes, just like a normal disease can set off Type 1 diabetes in a child predisposed to it. But the vaccine's adjuvants throw the whole system into a far larger response than it normally would give to any real infection. So the chances of a vaccine causing the virus to spread are much higher than an appropriately-modulated immune response to a normal pathogen. Not to mention that in the real world, you don't usually get Diptheria, Tetanus, Pertussis, Hepatitis B, and influenza all in the same day.
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