Wouldn’t make any difference if they knew or not. In general the US is unbothered by US citizens having or acquiring a second (or third, or fourth . . .) citizenship, unless this is done with the intention of renouncing US citizenship (in which case they’ll take the view that you have indeed renounced your US citizenship, as intended).
Similarly, a citizen of another country who is naturalised in the US is required to make a declaration renounce previous allegiances, but of course as a matter of law in the country of which he is already a citizen this declaration probably has no effect at all, and his previous citizenship status is unchanged. That country may well have a process under its own laws by which he could renounce citizenship; the US does not require him to go through that process in order to be naturalised in the US. The result is that a naturalised US citizen will commonly hold dual citizenship. The US authorities are fine with this.
If they knew they never showed any sign that they cared. On one of the tax forms I used to fill out (2555 I think) there was a line for nationality and I’d always put “dual US/UK”. When I would fly from the UK to US I’d check in with my US passport and then show that to passport control in the US. Coming back I’d check in with the US but then show the UK/EU one at passport control. I got to use the short queue where ever I went.
The last time I saw my US passport was went I went through the renunciation interview in London. I was hoping they’d send it back with the corner clipped off like they do for a renewed passport, but they kept it. That was the only time a US official asked to see my British passport to make sure I wouldn’t end up stateless.
The whole idea of nationalism and citizenship is an anachronism that has no useful place in modern political thought. Nationalism grew from the desire of a potentate to enforce tribute from his subjects, but never benefited the populace. Nationalism has no use in modern republicanism. Even today, nations use nationalism to enforce their own central authority over their citizenry, rather than the other way around.
Citizenship is an impediment, rather then a benefit. When traveling abroad, with different passports, why should a husband require a visa but not his wife? How can the nationality of the spouses possibly have any relevance to their freedom to travel?
Essentially, citizenship creates a global caste system, ,in which people are assigned at birth a status that can be shaken free of only with arduous effort and considerable resistance…