Or, even if possible, whether it would be useful for anything.
It might give us exact equations for solving any conceivable situation... but the equations themselves might be too complex for us to solve.
Oh, we're well beyond that point already. In quantum mechanics, for example, we will never be able to solve a 200 particle system exactly (on a classical computer). We will always need to go for simplifications and effective theories for larger systems.
A more general theory will most likely have to be more complex, as it has to replicate the behavior of quantum mechanics, that we see. So finding a universal theory and then calculating everything with it is never going to happen.