Do metals have negative permittivity(real part) at microwave frequencies?

I have been studying metamaterials from "ELECTROMAGNETIC METAMATERIALS:TRANSMISSION LINE THEORY AND MICROWAVE APPLICATIONS" by Caloz and Itoh. They have commented that metals at optical frequencies have negative permittivity. My question is whether metals at microwave, rf and other lower frequencies have negative permittivity too.

From the Drude model we have,

$epsilon(omega)=1-frac{omega^{2}_{p}}{omega^{2}+Gamma^{2}}+ifrac{omega^{2}_{p}}{omega^3+omega Gamma^2}$

So, it seems that for the real part of permittivity to be negative, $omega < sqrt{omega^{2}_{p}-Gamma^{2}}$. Therefore, if $omega_{p}$ lies in the optical range, then the real part of the permittivity should be negative at microwave frequencies. Am I right?