Have you tried using multi_normal instead of the cholesky version? The sum of cholesky factors is not the cholesky factor of the sum e.g \sqrt{2} + \sqrt{2} \ne \sqrt{4}.
No. Only when you apply sampling statements with nonlinear transformations e.g. log(x) ~ normal(0, 1). I think stan will warn you if you do something that it thinks might require a Jacobian transform.