Yes, Boxer, July, and Nada were all super big names in BW and each have multiple Starleague wins. They are all legends in their own right. But they were faded legends.
Boxer was at his best in the early 2000s as a player, but became larger than life as an e-sports personality because of his actions outside the game. When people say he helped build e-sports, they mean that quite literally. He was a MAJOR factor in the establishment of the modern team structure and sponsor acquisition, and even managed to lobby the government to create a team in the form of Air Force ACE, where select progamers could complete their military duty without abandoning the game. Boxer is the biggest name in BW because without him, its very unlikely the e-sports model Korea has now would have ever been established.
Nada and July were more known as players only, but both were extremely dominant at certain times. They each had multiple periods of extreme strength, but the vast majority of their combined careers is pre-2007. July had 1 amazing run in 2009, taking an OSL, but it was sort of a flash-in-the-pan comeback, and was not really representative of his play on either side of the run. They both could be counted on to take some wins in proleague every now and again, but they had already long lost the BW-equivalent status of Code S even by mid-2009, well before SC2's release and their transition.
The only other Starleague winner that has transferred (at least that I can remember.. certainly the only relevant one), is ForGG who also took his win in 2009 (within a month of July's win actually). He pioneered a very timing-heavy style and took out some major names including Jaedong in the finals. But he peaked really early and fell very quickly. He seemed to drop completely off everyone's radar within half a year and had quickly faded back into the mediocrity.