I guess Warren probably would have been able to convince Vinson too?
Warren wouldn’t have been appointed yet. Felix Frankfurter believed that Vinson’s death changed the game
It definitely changed the game. The rumor was that it was initially 5/4 to desegregate without Warren, with Black, Douglas, Minton, Burton, and Frankfurter for desegregation, and Vinson, Clark, Reed, and Jackson dissenting. Jackson was apparently conflicted and might well have flipped to make it 6/3, though it's well documented he was initially opposed. Needless to say, it would have been much more challenging to make a 5/4 decision stick. It was challenging enough when it was unanimous.
With Vinson dissenting, Justice Black would have been the most senior justice in the majority and would most likely write the opinion. Assuming a 5/4 Brown sticks, I would expect Hugo Black to be much more widely known and remembered as the St. Paul of civil rights. His "conversion" would have been decisive.