Pretty much. Golden Age Cap was just Batman with a secret identity as an incompetent private in boot camp. Except for a few stories (notably the first Red Skull appearance and the Dragon of Death in issue 5) he was never portrayed as an active full-fledged member of the army, he was just in basic and never saw combat. As Cap, he was wanted by the police and the upper army was suspicious of him, though this occasionally varied like a story where he was sent to help promote war bonds.
The vast majority of his GA stories had him acting as a detective and monster hunter, fighting fake monsters Scooby Doo-style, gangsters, inheritance murderers, mad scientists and gothic horror villains. Even Red Skull himself was just a variation of these types of phony monsters (and his first appearance is clearly inspired to some extent by The Joker's in Batman #1). Bucky actually saw more combat on foreign soil with The Young Allies. Cap's only recurring villain besides Red Skull was The Black Talon, a Mexican painter who lost his hand in a car accident and had the hand of an executed black murderer transplanted onto his stump, which made him evil.
If anything, the modern portrayal of Cap as a soldier fighting spies and going behind enemy lines comes from the 1950s Cap, who was later made into a crazy racist impostor.