Hi Ross,
It does that automatically, whenever the integration is enabled.
For example, if I search for “test”, then I get these page results in the drop-down. When I hit enter, I get redirected, and the results are the same on the results page.
Some differences can be expected, usually when a non-post type is returned in the drop-down, or if a post type is not fully supported in the grid, but generally it should be very similar.