I know the IKEA brackets.
The two stub screws simply hold the friction plate to the chipboard.
You then put on the adjuster plate (small 1-inch square thing with
keyhole shaped hole) and pull the wall fixing tight. This pulls the
entire back of the cupbaord against the wall.

All the force of the wall fixings is in the 1 inch sqaure at each top
corner. If I were you I'd use larger plates so the force is distributed
over a much larger area, then you should be ok.

What actually keeps the cupboard to the wall is the lateral foce
(friction) between the back of the cupbaord and the wall.