No.  For  example, the spectral radii of 
$$ A = \pmatrix{0 & 1 & 3\cr 1 & 0 & 3\cr 0 & 0 & 0\cr},\ A' = \pmatrix{0 & 0 & 5\cr 1 & 0 & 3\cr 0 & 0 & 0\cr}$$
are  $1$ and $0$ respectively.