YMMV with ground wires in the paper Romex. This house (SW Fl) has the smaller ground (1963) and the house I grew up in (DC area) had the same reduced ground in paper RX built in 1953. It was only connected to the box. NEMA 1-15 receptacles throughout.
If you plugged in the 5-15 adapter and hooked up the ground wire you did have a ground.
