I mean I think half the time it does and half the other time it doesn't mean Conqueror's Haki. you have times like when Jinbei just grabbed Who'sWho's wrist and there was black lightning. So definitely that black lighting has nothing to do with Conqueror's Haki.
But then there are other times that Conqueror's Haki has been
clearly signified by Black lightning. Like that time Shanks used wifi Haki on green bull. or when Luffy first went to gear 5 and his Conqueror's Haki was knocking people out.