We establish criteria on the chemotactic sensitivity $χ$ for the non-existence of global weak solutions (i.e. \textit{blow-up} in finite time) to a stochastic Keller--Segel model with spatially inhomogeneous, conservative noise on $\mathbb{R}^2$. We show that if $χ$ is sufficiently large then \emph{blow-up} occurs with probability $1$. In this regime our criterion agrees with that of a deterministic Keller--Segel model with increased viscosity. However, for $χ$ in an intermediate regime, determined by the variance of the initial data and the spatial correlation of the noise, we show that \emph{blow-up} occurs with positive probability.