Well, if you consider that the movies were really more based on the comic book than the Howard stories, then no, they weren't untrue to the source material (ie, the comics, where Conan can't even pronounce Red Sonja's name correctly).
However, having read Howard's stories, I really have to say the movies do quite an injustice to the character and the spirit. Howard was really sort of an action writer. Much of the original Conan kinda drags on. I liked the end, but even that isn't too true to Conan (actually more true to the A-Team), especially where Conan prays to Crom, which I get the impression was actually a no-no. Even though it is a heck of a cool line.
And while I am quite fond of Conan the Destroyer, it's incredibly campy. Something definitely not in Howard's stories.