Actually, I don't think that will happen with standard brakes. Disc brakes on the other hand would cause that condition. My mind wandered off on this topic on my ride to work this morning.

Assisted by dabac's pictures, I concluded that the only leading and only trailing spoke pattern's downfall is that any displacement of the hub (such as hitting a bump or using a rim brake or even simply sitting on the bike) will apply a torque to either side of the hub flange. These torques will be equal and opposite so as long as the hub shell can stand up to those torques it will be ok (obviously from dabac's pics, that hub couldn't take it and I doubt many others can either).

Applying a torque to a hub laced like that would cause all sorts of problems though it would eliminate some of the internal twisting force on the hub (due to the reduction in tension on the leading spokes). Any torque applied to the hub would be taken completely by the trailing spokes (hopefully they are on the side that is having the torque applied to it) and thus be applied complete to one flange of the hub. This would reduce tension on all of the leading spokes which would, as Mark Kelly commented, cause the hub to shift relative to the rim. Not a good thing for either a rear wheel or a front disc brake wheel.