I concede, the work is a novel of its day, and would resemble many an English gentleman, but not a direct result of anybody's particular life.

The coincidental similarities with the Prince include an indisposed father, a spoiled and willful nature and a secret engagement/wedding.

Then this passage from the final chapter shows the inference of the day tjat if you were nobility, you could "bleach" away the illegitimacy.

"Such was the blood of gentility which Emma had formerly been so ready to vouch for! It was likely to be as untainted, perhaps, as the blood of many a gentleman: but what a connexion had she been preparing for Mr. Knightley, or for the Churchills, or even for Mr. Elton!

The stain of illegitimacy, unbleached by nobility or wealth, would have been a stain indeed."