1. Ground effect occurs within one wingspan of the ground. So while the high wing of the Bae 146 (and C-17 and C5A/B) reduces GE a bit, there is still quite a bit of GE from an 86-foot wing 15 feet or so above the ground.
2. Ground effect is a two-edged sword. One can take off in ground effect without sufficient speed/lift to maintain flight outside ground effect. (cf. Ekranoplans, etc.) There have been a certain number of accidents tied to overloaded aircraft (not any particular type) that got off the runway in GE, but could not then climb high enough to clear obstructions.
I guess what I see in the 146 is that the reduction in ground effect due to a high wing, is countered by the increased wing and flap effective area due to the wing being less interrupted by a fat fuselage.
Wiki sometimes oversimplifies a bit, and I'd say the 146 design was intended to enhance good "unimproved airport" capability - no jetways, poor runway surfaces. And since such airports likely also have short runways - high overall TO performance (not necessarily through ground effect).
Whether it actually did so or not, I leave to others who've flown it.