No Schengen stamps if you already live in the Schengen area. Unless there is data sharing the US gov wouldn’t be able to see it from a passport.
I suppose it will be another question on the form. Next to ‘I am not a terrorist’
As a side-note: I saw the forms that my great grandparents had to fill out when entering the US from Europe back in 1905 or thereabouts. There was a checkbox for "anarchist"