Unlike some other posters, I was only talking about what convolution can do in theory.
EQ and phase changes are possible. Time delay is a kind of phase change, so it is possible. Combinations (sums) of these effects are possible, which include things like adding or canceling out echos/reverbs.
Harmonic distortion, which adds harmonic frequencies as a function of the fundamental frequency, is not possible. If the input to your convolver is a pure sine wave, the output can only be a pure sine wave with the same frequency.