Regardless of the gravity canceling out in this region (which is more complicated and probably will not happen). The current LIGO and Virgo wouldn't have enough spatial resolution to pinpoint tiny regions between black holes.
To explain what will happen is that gravitational field in region you are describing would have a steep spacetime curvature and a point where it will cancel gravitational forces would be more of a saddle (lagrange point classically) point rather than zero gravity region.
Now you also have quantum fluctuations that now with this strong gravitational field you will have virtual particle - anti particle paris pop in and out of vaccum. This is not going to be only in thia region but all around. Also merging process will enhance this phenomenon but deciding where actually this middle point will be difficult.
Now it would be impossible at least for our current observational tools to have resolution for the scale we are talking about. Event horizon telescope for example is designed to observe areas around singularities on much larger scales that what you are interested in here.
But the interesting part would be If matter and antimatter pairs were produced between merging black holes, they would likely be short-lived. In this intense gravitational environment, any particles created would be rapidly torn apart or accelerated towards one of the black holes. The annihilation of such pairs might emit gamma rays, but this signal would be extraordinarily faint compared to the other high-energy processes occurring during a black hole merge.
So the answer is probably No, at least with our current technology.
Gravity is not a force in GR. The spacetime curvature in a spacetime with two black holes that merge is not describable in terms of a simple "gravitational field". Spacetime curvature is a fourth rank tensor with twenty independent components. In vacuum ten of those vanish identically, leaving ten independent components.
To explain what will happen is that gravitational field in region you are describing would have a steep spacetime curvature and a point where it will cancel gravitational forces would be more of a saddle (lagrange point classically) point rather than zero gravity region.
Now you also have quantum fluctuations that now with this strong gravitational field you will have virtual particle - anti particle paris pop in and out of vaccum. This is not going to be only in thia region but all around. Also merging process will enhance this phenomenon but deciding where actually this middle point will be difficult.
Now it would be impossible at least for our current observational tools to have resolution for the scale we are talking about. Event horizon telescope for example is designed to observe areas around singularities on much larger scales that what you are interested in here.
But the interesting part would be If matter and antimatter pairs were produced between merging black holes, they would likely be short-lived. In this intense gravitational environment, any particles created would be rapidly torn apart or accelerated towards one of the black holes. The annihilation of such pairs might emit gamma rays, but this signal would be extraordinarily faint compared to the other high-energy processes occurring during a black hole merge.
So the answer is probably No, at least with our current technology.