  This work presents and analyzes electrical resistivity data on the organic
superconductor (TMTSF)$_2$ClO$_4$ and their anion substituted alloys
(TMTSF)$_2$(ClO$_4$)$_{1-x}$(ReO$_4$)$_x$ along the least conducting $c^\star$
axis. Nonmagnetic disorder introduced by finite size domains of anion ordering
on non Fermi liquid character of resistivity is investigated near the
conditions of quantum criticality. The evolution of the $T$-linear resistivity
term with anion disorder shows a limited decrease in contrast with the complete
suppression of the critical temperature $T_c$ as expected for unconventional
superconductivity beyond a threshold value of $x$. The resulting breakdown of
scaling between both quantities is compared to the theoretical predictions of a
linearized Boltzmann equation combined to the scaling theory of umklapp
scattering in the presence of disorder induced pair-breaking for the carriers.
