A module \(M\) is said to be virtually Cohen-Macaulay if its virtual dimension (the minimal length of a virtual resolution) is equal to its codimension. This main result outlined in this short note is the following: If \(S\) is the Cox ring of \(X= \mathbb{P}^{n_1} \times \cdots \times \mathbb{P}^{n_r}\) and \(\Delta\) is an \(r\)-dimensional simplicial complex whose associated variety \(V(I_{\Delta}) \subseteq X\) is equidimensional, then \(S/I_{\Delta}\) is virtually Cohen-Macaulay. The note contains many colorful examples of these virtually Cohen-Macaulay Stanley-Reisner rings as well as an example of a quotient ring \(S/I\) which is not virtually Cohen-Macaulay but \(S/\sqrt{I}\) is virtually Cohen-Macaulay. The final section discusses two different ways to construct new virtual resolutions from a given virtual resolution.