Does metric signature affect the stress energy tensor?

If one were to derive the stress-energy tensor for a metric with $(+,-,-,-)$ signature would it be different from the stress-energy tensor derived from the same metric but with $(-,+,+,+)$ signature?

The sign convention for the stress-energy-momentum (SEM) tensor $T^{\mu\nu}$ is usually chosen such that the energy density $T^{00}$ is positive.
$$\tag{1} T^{\mu\nu}~:=~\pm \frac{2}{\sqrt{|g|}}\frac{\delta S}{\delta g_{\mu\nu}}, \qquad T_{\mu\nu}~:=~\mp \frac{2}{\sqrt{|g|}}\frac{\delta S}{\delta g^{\mu\nu}},$$ for Minkowski sign convention $(\mp,\pm,\pm,\pm)$, respectively.