In 1519, Henry VIII's mistress Bessie Blount gave birth to the King's natural and only living son at the time, Henry Fitzroy, who was made the Duke of Richmond. Now what if this son had been born a girl? Would Henry have recognized her as his daughter? And what of her future? Would Henry have married her off? And to whom?
Henry Fitzroy, Duke of Richmond, was the only illegitimate child of Henry VIII's that was public knowledge.
However there were other children that were suspected of being his including:
Catherine Carey, daughter of his mistress Mary Boleyn, the sister of his second wife, Anne Boleyn, and wife of William Carey.
Henry Carey (4 March 1526 – 23 July 1596), brother of Catherine.
John Perrot (November 1528 – 3 November 1592), his mother being Mary Berkeley the wife of Sir Thomas Perrot
Thomas Stucley (c. 1520 – 4 August 1578), his mother being Jane Pollard the wife of Sir Hugh Stukeley
Richard Edwardes (1523? - 1566), born to Mrs. Agnes Edwardes
Ethelreda Malte (born c. 1527), born to Joan Dingley, alias Dobson. Paternity was claimed by John Malte.
I would very much doubt that in 1519, he would be as proud to boast of having a bastard daughter so this new daughter, Elizabeth Blount would just be another suspected child.
She would most likely be kept away from marrying and giving birth to a male heir that could out do, Mary Tudor.