Changing aperture has the same overall effect on depth-of-field with a tilted lens that it has on an untilted lens.
Tilting a lens changes the visible consequences of any change in aperture because it (when viewed sideways) changes the shape of the in-focus area from a rectangle to a wedge (with the point towards and above/below or below the camera, depending on tilt direction). The diagrams on this page include some good visualisations of the effect.
decreasing/increasing the aperture (increasing/decreasing f-number) effectively causes the width of the base of the wedge to increase/decrease accordingly. This results in the effect of the change in aperture becoming progressively smaller close to the point.