It's definitely outside of the realm of known physics, but it's not that far beyond how resonant cavity thrusters supposedly might work. RCTs appear to violate conservation of momentum, but might work by pushing against virtual particles to generate thrust.
Now, based on our current understanding of physics, that shouldn't work, and it shouldn't be possible to generate usable force from a vacuum, or to break the symmetry of particle formation from a vacuum.
If, however, you had a means of causing the vacuum in front of you to generate a temporary imbalance in virtual particles, those particles would have mass, in a similar way that the particles providing the thrust in and RCT gain mass. Those particles would have gravity, and as such would exert a small pull on your ship. Again, that violates the laws of physics as we currently understand them, and probably couldn't happen.
Even if that did work, though, the forces involved would be incredibly small. Gravity is a VERY weak force, and generally huge amounts of matter are required to actually create noticeable effects. Either large amounts of matter, or incredibly dense matter, would be required for any significant acceleration. Your best bet would be to cause microscopic black holes to coalesce just in front of your ship, where they'd exert a reasonably strong force for a brief moment before popping back into nothingness. Even so, this type of drive would likely be best for long voyages, where a ship could spend days or months steadily accelerating, rather than for anything requiring quick, precise acceleration.
All of that, again, is probably impossible, but it's about as close as you can get to reality for a drive that's generating gravity wells to accelerate your ship in violation of half the laws of physics.