There are five series of the original radio show. So far as the radio show is concerned, the answer to your question is no.
Deep Thought does mention that Earth's computer program, to find the answer to the ultimate question, was terminated 5 minutes too soon (five minutes before the moment of read-out) due to the destruction of Earth by the Vogons. But this has nothing to do with the girl's discovery.
According to radio series one, the girl (later, in series 3, she is identified as Fenchurch, and becomes Arthur's girlfriend) has only realised how the Earth can be made a good and happier place; she has not discovered anything relating to the computer program, nor about the ultimate answer.
... then, one Thursday, nearly two thousand years after one man had been
nailed to a tree for saying how great it would be to be nice to people
for a change, a girl sitting on her own in a small café in Rickmansworth
suddenly realized what it was that had been going wrong all this time,
and she finally knew how the world could be made a good and happy place.
This time it was right, it would work, and no one would have to get
nailed to anything.
In fact, she never tells anyone her solution, not even Arthur. So we never get to know why she got so excited.
And in Fit the Sixth we learn that the computer program got cocked-up by the arrival on Earth, in its prehistoric dawn, of the Golgafrinchams on their B-Ark -- causing the original cavemen to die out, who were a key part of the computer program that was designed to find the answer to the ultimate question (of life, the universe, and everything).
Bit of a waste of time for the Vogons, blowing the planet apart, when the computer program had in fact been wrecked 2 million years earlier.