Accessing owner of PlayerState on multiplayer client

No, but what you could do is something like this, declared in your custom PlayerState header.

HEADER
-------------
DECLARE_DELEGATE(FOnPlayerColorChange)

class AMyPlayerState : APlayerState
{
	GENERATED_BODY()
public:
	UPROPERTY(ReplicatedUsing=OnRep_Color)
	FLinearColor PlayerColor;
	FOnPlayerColorChange OnColorChangeDelegate;

	UFUNCTION()
	void OnRep_Color();
};


SOURCE
-------------
void AMyPlayerState::OnRep_Color()
{
	OnColorChangeDelegate.ExecuteIfBound();
}

And then in your custom Pawn header.

HEADER
-------------
class AMyPawn : APawn
{
	GENERATED_BODY()
public:
	virtual void PostInitializeComponents() override;
	void OnPlayerColorChange();	
};


SOURCE
-------------
void AMyPawn::PostInitializeComponents()
{
	Super::PostInitializeComponents();

	AMyPlayerState* MyPlayerState = Cast<AMyPlayerState>(PlayerState);
	MyPlayerState->OnColorChangeDelegate.BindUObject(this, &AMyPawn::OnPlayerColorChange);
}

void AMyPawn::OnPlayerColorChange()
{
	AMyPlayerState* MyPlayerState = Cast<AMyPlayerState>(PlayerState);
	FLinearColor NewColor = MyPlayerState->PlayerColor;
	//DO COLOR RELATED STUFF
}