Morgoth to
Hurin:
"Behold! The shadow of my thought shall lie upon them wherever they go, and my hate shall pursue them to the ends of the world."
Hurin to Morgoth:
"You speak in vain. For you cannot see them, nor govern them from afar: not while you keep this shape, and desire still to be a king visible on earth."
Was it the curse which caused Beleg to accidentally poke
Turin's foot while cutting him free (leading to Beleg's death by Turin)?
Was it the curse which caused Turin to unknowingly sit at Saeros's accustomed seat at the dinner table (leading to Saeros's death)?
The exchange between Morgoth and Hurin suggests that initially Hurin did not believe Morgoth's curse had any meaning. Although, at the end of his life I think Hurin came to believe otherwise.
On my next read-through of
The Children of Hurin, I'll have to keep this question in mind: "Did the curse itself have any real effects on Turin?" I'll probably conclude that there's no way to know for sure. (That's the trouble with curses...you never really know.)