Effects of DC offset on a signal
In a mathematical sense it doesn't but (almost) any nonlinear interaction, say modulation or demodulation, will cause additional signals, leakage/out of band, signals.
The point is that when you do the evaluation you must include the modulator or demodulator; as well as things like transformers which will be biased off center and thus generate extra distortion.  It's the non-linearities in the overall signall path that induce extra signals.  By definition of the Fourier/Laplace transform superposition and linearity properties a linear system will not generate extra signals.