Obviously it’s not true 100% of the time. If it were, then people will terminal illnesses would pray for recovery on Purim and miraculously recover.
I know a gentlemen who’s father fell down a flight of stairs on Purim a number of years ago. While I can’t state for a fact that he davened for his father’s recovery on Purim, I would be extremely shocked if he told me that he didn’t. Sadly, his father did not recover and passed away a few days later.
Of course, that’s not to say that prayers aren’t answered on Purim. But to answer the OP’s question plainly, the answer is clearly no.
The Wolf