Not quite..
The more flap you use the shorter the takeoff roll. At low speeds (such as T/O runs) the drag is much less of a factor than the increased lift. So the more flap you put out the shorter the t/o roll will be in distance over the ground. At full flap you have alot of drag so i suppose there may be a slight increase in ground roll, but it would be relatively minor i would think. Anything in the t/o flap setting range is always more flap=less ground roll regardless of the drag increase.
The shorter your t/o run you get airborne at a lower speed. That kills your climb cause you have to accelerate much further towards best rate of climb speeds than if you got airborne with zero flaps for example. At this point the drag of the extra flap becomes an issue in accelerating the aircraft towards best rate of climb. That and the fact that the speed you got airborne at is much lower means you sepnd more time accelerating forward than climbing upward and your 2nd segment climb suffers.
You're basically trading energy you would have gained on the ground for getting airborne earlier the more flap you put out.