Here is an illustration of the concept of tilt movement. The usual DOF for a conventional lens is represented by the untilted blue dotted rectangle. The camera's focal plane is the rightmost vertical gray rectangle. The untilted lens and the tilted lens are apparent via the illustration. Our targets are three trees, represented by the green arrows, and focus is on the middle tree...let us just assume it has 20' DOF thickness so the front and the rear green arrows are outside the DOF zone.
We see the tilt occurs thru the optical axis of the lens, which is what happens on a Canon tilt lens. When we tilt, the center of FOV looks downward compared to the untilted lens. According to the Schleimpflug principle, there is a optical pivot point which is below
the camera. So the plane of focus at the subjects rotates about that pivot point, as does the DOF zone. The DOF zone started as a perfect rectangle, but we see that the DOF of the tilted lens now has a trapezoidal shape. Note how the trees now fall within the (same, but trapezoidal) DOF zone. So more of the ground is within the DOF zone, and all three trees fall -- but only partially, in terms of their height -- within the DOF zone.
So, yes, tilt could increase the amount of ground within the DOF zone, but you could at the same time be hurt by the TALLNESS of objects in the photo.
(BTW this illustration is not meant to be technically absolutely correct, but is intended to convey fundamental concepts behind tilt movement.)