Hm. Not so much the Feldgendarmerie I think, they're more like military police in times of war and regular police in times of peace. They'd mostly served in occupied regions for security.
However, Austria's Evidenzbureau and Prussia's Geheimpolizei are more relevant places for inspiration and sources for training, since both deal with intelligence gathering, counter-espionage, and national internal security.
True. I could see the United States Military Police taking notes from their counterparts in the Fledgendarmies and even adopting similar uniforms with the neck chain.
Though they mainly saw action in holding down the Canadian and Confederate boarder territories during the interwar and second great war. Where they earned a brutal reputation for crushing dissidents and hunting down suspected rebels.