The formula in Nogueira's answer tells the story.
For example, in positron electron annihilation, they form a photon which might eventually decay into another two particles.
In the formula we see a pole in the complex plane. Crossections are real numbers and calculating the square of the amplitude will give real numbers in the formula, which is the Breit-Wigner formula.
Can we calculate the resonant cross section for this process with the Breit Wigner Formula as well?
A virtual particle, even though it is described by this pole, is not represented by a real function, so cannot be interpreted as a cross section , it is part of the integration that will give a cross section. Within the integral it is off mass shell for the particle it is describing, i.e. the virtual photon in the question. Even the specific resonance plotted within the integral is like a mountain in the complex plain. It is only the integration which can relate the pole with physical crossections, and virtual particles disappear .
A virtual particle, even though unphysical in energy and momentum carries the other quantum numbers identifying particles, as spin , charge etc, that is why it is useful in drawing Feynman diagrams that are a shorthand for the integrations that give cross sections. One should not confuse it with a real particle because its manifestation is in the unphysical complex plane. It is after the integrations are carried through that the effect of the pole in the propagator can be compared with data/cross-sections.