Vacuum energy is as good an explanation as any for what Dark Matter is. The current consensus hypothesis for what Dark Energy is, is centring around Vacuum Energy. So it wouldn't surprise me that Dark Matter might originate from the same source too! Some theories already suggest a common origin for both phenomenon.
So why would virtual particles produce extra gravity, if they just flit in and out of existence so quickly that we can't even measure it? Well, likely at galactic distance scales, billions and billions of virtual particle appearances might create very brief gravitational effects that disappear again. So within small scales, such as the planetary or solar system scales, these things don't last long enough to be a worry. But at galactic+ scales, these things like produce gravitational waves that are traversing at the speed of light and take a long time to disperse. It takes light a 100,000 years to traverse the galaxy, so it should take the same amount of time for a virtual particle's gravitational wave. Obviously each virtual particle will produce negligible gravity, but billions upon billions may produce an accumulative effect, and the effect will last essentially forever, as virtual particles are always appearing and disappearing everywhere.