Downforce on the back doesn't create lift in the front, unless there's a torsion created by the shape of the wing (down in back, up in front)... which would more likely tear the wing off the car at high speeds... not a feasible wing design.
Increased downforce in the back with no adjustment up front does, however, create an imbalance in the way the car handles. The back has much more grip than the front now... so in hard turns, you will have serious understeer, and the inside front wheel may even lift off the ground completely!
This can be easily balanced out by augmenting the aero in the front too.
EDIT: for the record, though... you're right... "just slapping a wing on a car" is more likely detrimental to the overall performance... as it increases weight, increases the Cf (friction coefficient), decreasing top speed, and can create imbalance in handling, even if it effectively increases downforce (making the car harder to drive).