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 the camera). The diagrams on [this](http://www.cambridgeincolour.com/tutorials/tilt-shift-lenses2.htm) 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.