These concepts refer to completely different aspects of reality. Supersymmetry is a (possible) symmetry of the microscopic laws of Nature, much like the rotational symmetry.
Entropy is the quantity counting the disorder of a given (usually macroscopic) system, the number of rearrangements that don't change the macroscopic appearance of the physical system (well, the logarithm of the number of these rearrangements).
Entropy may be zero or nonzero for a system that preserves some supersymmetry or doesn't preserve any supersymmetry, entropy may be zero or nonzero in a theory that is supersymmetric and in a theory that is non-supersymmetric. All the combinations are surely possible. Supersymmetry is a particular property of theories (or states), a constraint, but it doesn't prohibit macroscopic objects. Entropy is a measure of any macroscopic physical object.
Some calculations of entropy may simplify in a supersymmetric theory, especially if the state of the physical system preserves some of the supersymmetries. (For example, the Strominger-Vafa black hole in 5D is the first one whose entropy was computed microscopically, and it's largely because it's the simplest black hole with a classically nonzero horizon that still preserves some SUSY, i.e. it is BPS, we say.) But that's true for all calculations, not only entropy calculations: SUSY often constrains and simplifies things.