There's no particular need, from a physics perspective, to have dihedral in an airplane. It's there for stability. If you roll to one side, you naturally start slipping to that side. In an aircraft that has a positive dihedral, this slip means the lower wing will have greater lift than the upper wing. This creates a rolling moment back towards level.
An anhedral (negative dihedral) wing would have the opposite effect, increasing roll rate away from level. Note that this isn't necessarily a bad thing: it's possible for planes (such as the An-225) to be too stable, and thus, too difficult to roll when you actually want to. Having anhedral wings fixes that issue.
But there is another effect. Both dihedral and anhedral slightly reduce lift. Since the lift vectors of each wing aren't parallel, a small portion of the lift the wings might have generated is lost. This translates into slightly higher stall speeds, and slightly more drag.
In short, any "good" that the two opposite sets of wings might do would cancel each other*, while the "bad" would add together. You could get such an airplane to fly, it would just be less efficient than it otherwise would have been.
*Of course, if they're not at equal angles, or one is bigger than the other, or they have different airfoil shapes, etc., then they won't perfectly cancel, and you'll still get some effect based on which one is "stronger".