No, they didn't, but they weren't socialist either.
The original party was a diverse coalition of shitty people, some of whom considered themselves socialists because socialism isn't, outside of the Americas, considered a "bad word", especially in a Europe that was having trouble adjusting to a world war and unfettered capitalism during the industrial revolution. Workers rights are not a bad thing. It had, by that point, been watered down to practically a feel good term, the way "Freedom" is in the US.
Anywho, the socialists within the party pushed to have "Socialist" put in the name. Hitler opposed this. He was out numbered.
Then during the Night of the Long Knives, Hitler had the entire self-described socialist wing of his party purged. Its leaders were executed.
TL;DR - the party wasn't a socialist party, it had that in the name for historical reasons, Hitler hated it but by the time the party rose to power it was too late to do anything about it. But he did do something about the socialists in his party, and it wasn't pretty.