The comments give you the gist of the answer. Virtual particles cannot create some particles, including radiation due to their annihilation unless there is some external factor that causes some real energy to appear.
Prof Strassler's link by @countto10 has a good description of what are virtual particles and ways in which their effects can be real. In essence they really are disturbances in quantum fields, which when in certain ways affected by something else can cause an observable effect. Three good examples are
1) the Hawking radiation you mentioned and gradstudent explained. It is only because the strong gravitational field from the Black Hole interacts with them that one of them can be thought of as having negative energy and goes into the Black Hole that the other one escapes, with a real energy, towards infinity. The one that falls in substracts from the Black Hole mass. Another way of describing and calculating the process is that it is quantum tunneling from inside the horizon, where a particle tunnels out. In either way of looking at it the energy came from the energy (and thus mass) of the Black Hole.
2) a Quantum Field Theory process such as the Coulomb interaction between a positron and electron (or any cried particles). The virtual particle explanation is that a virtual particles gets exchanged between the two, and causes energy and momentum to be exchanged between them. That's the Feynman diagram view. Another view is that as they pass close to each other they disturb the electromagnetic field which interacts with them to have energy and momentum exchanged. In the latter point of view it is not a virtual particle that makes the effect, but a virtual quantum field, the vacuum electromagnetic field, which gets disturbed and causes those effects on the particles. In Quantum Field Theory this gets denoted by an interaction term in the equations for the scattering of a charge by another.
3) a third example is a charged particle moving along, in vacuum, and randomly interacting with the vacuum electromagnetic field, polarizing it and being affected by it. A Feynman diagram as Prof Strassler's explains in the link denotes this by a spontaneous loop that ends the electron (or whatever charge) line and quickly restarts it. That loop represented virtual photons. They have to be taken into account in accounting for the real mass of the electron, along with other possible loops and 'internal' processes. All those internal a processes are virtual particles. None of those exist where the virtual particles escape out, i.e. Become real particles. Prof. Strassler's explanation shows the diagrams and explains it well. It is part of renormalizing the particles mass from so called 'bare' to 'dressed'.
Vacuum spacetime cannot create something out of nothing where you can detect it, but can certainly interact with real particles (or various other mechanisms you might invent, the environment) to have an effect on them. It is dependent on the existence of quantum fields in vacuum which are in their vacuum states but which can be affected by anything else interacting with them.