Possibility that the cube is solvable

[cuBerBruce]

The only kind of unsolvable parity you can get on even cubes is CO parity, so yes.

Unless you're solving as a supercube. For a 4x4x4 supercube (where each center must must be solved to an exact location rather than just a particular face), the probability would be 1/6 (corners and centers must have the same parity).