Booker seems to be the most likely black candidate to run, but it's certainly *possible* that, say, Kamala Harris or Deval Patrick also run.
In any case, we don't know that blacks will block vote for any one candidate in 2020. However, it is true that black candidates running for the Dem. nomination for president always overperform among blacks relative to whites. Heck, even Al Sharpton in 2004, who was an asterisk with white voters, managed 17% of the black vote in South Carolina:
http://www.cnn.com/ELECTION/2004/primaries/pages/epolls/SC/So yes, one would presume that South Carolina will be one of Booker's better states.
But just because Obama '08 was strong among both blacks and "wine track" whites doesn't mean that Booker would be able to replicate his strength among both groups. Seems likely that the white Obama '08 primary voters will have other options.