According to Richard Dawkins' 'The God Delusion', no, she did not.
Excerpt from the book:
Peter and Jean Medawar,* in The Life Science, attribute the following version [of the Beethoven Fallacy] to Norman St John Stevas (now Lord St John), a British Member of Parliament and prominent Roman Catholic layman. He, in turn, got it from Maurice Baring (1874-1945), a noted Roman Catholic convert and close associate of those Catholic stalwarts G. K. Chesterton and Hilaire Belloc. He cast it in the form of a hypothetical dialogue between two doctors.
'About the terminating of pregnancy, I want your opinion. The father was syphilitic, the mother tuberculous. Of the four children born, the first was blind, the second died,
the third was deaf and dumb, the fourth was also tuberculous. What would you have done?'
'I would have terminated the pregnancy.'
'Then you would have murdered Beethoven.'
The Internet is riddled with so-called pro-life web sites that repeat this ridiculous story, and incidentally change factual premises with wanton abandon. Here's another version.
'If you knew a woman who was pregnant, who had 8 kids already, three of whom were deaf, two who were blind, one mentally retarded (all because she had syphilis), would you recommend that she have an abortion? Then you would have killed Beethoven.'
This rendering of the legend demotes the great composer from fifth to ninth in the birth order, raises the number born deaf to three and the number born blind to two, and gives syphilis to the mother instead of the father. Most of the forty-three websites I found when searching for versions of the story attribute it not to Maurice Baring but to a certain Professor L. R. Agnew at UCLA Medical School, who is said to have put the dilemma to his students and to have told them, 'Congratulations, you have just murdered Beethoven.' We might charitably give L. R. Agnew the benefit of doubting his existence - it is amazing how these urban legends sprout. I cannot discover whether it was Baring who originated the legend, or whether it was invented earlier.
For invented it certainly was. It is completely false. The truth is that Ludwig van Beethoven was neither the ninth child nor the fifth child of his parents. He was the eldest - strictly the number two, but his elder sibling died in infancy, as was common in those days, and was not, so far as is known, blind or deaf or dumb or mentally
retarded. There is no evidence that either of his parents had syphilis, although it is true that his mother eventually died of tuberculosis. There was a lot of it about at the time.