There is actually a window of time where that may be the case - more susceptible to infections in general as apparently they contain an immunosuppressant to allow the flu vaccine to actually get into the body vs. it being immediately intercepted and wiped out upon entry by the immune system and therefore be completely ineffective.
I did not know that. But if it gets immediately wiped out by the immune system that would be a good thing, no? Shows your immune system works.