That lawyer in Utah …
As you can see from the article, the author (Tom Leonard) knows the answer to be in the negative because the Royal Marriages Act 1772 precludes the descendants of George II from marrying without the sovereign’s consent – that sovereign being George III at the time.
James Ord’s putative ancestor is another James Ord, born in 1786, whose parents were supposedly the future George IV and Mrs. Fitzherbert (nee’ Smythe), yet only daughters have traditionally been attributed to them:
Of course, there are more established aristocrats in the USA. The current Earl of Essex is a retired teacher and septagenarian bachelor whilst his heir presumptive is a retired grocery clerk:
For comparison, the only known male line descendants of George III are from Germany, as his son Ernst returned to become King of Hanover: