Larry is a very interesting character in the play. We might say he becomes especially interesting and important considering Miller's project in this play. As he described it, he was trying to find a way to solve the theatrical problem of "dramatizing the past".
As Larry is a figure of the past, who does not appear in the play except by name and through a letter, Larry is a significant part of the solution to the problem Miller set out to solve.
However, we cannot argue that Larry is the root of the conflict that drives the play. Joe Keller is the figure who committed a crime - which is also an element of "the dramatized past" - and it is this crime that truly animates the play.
The conflict between Kate and Chris is essentially derived from Joe's sale of fraudulent airplane parts. Kate cannot believe that Larry is dead because, believing this, she feels she will also have to believe that Joe is responsible for Larry's death. For this reason, Kate clings to an insistent belief that Larry will be returning home and Chris should not marry Ann, Larry's former girlfriend.
Given this view of the conflict between Chris and Kate and Ann, we are able to recognize that Larry is not the character driving the conflict between Chris and Kate. Joe is the character who drives this conflict, and all the conflicts of the play, as a result of his crime.