Does "the governed" also refer to the enslaved?
If you want to play that game, then the US was not legitimate since only White Male Landowners over 21 could vote at the time of its founding. It was many many years before a majority of the adult residents could vote....well into the 20th century. Something tells me you would not find the United States illegitimate until about 1919 or so.
“Does “the governed” also refer to the enslaved?”
No; the concept of “consent of the governed” was not a reference to slaves voting for wage and hour laws.
At least I don’t know of any signers of the DOI that argued that slaves were brought to this country to be electors.
Maybe you know otherwise.