Very little if anything. The sound quality is affected by the bore profile (change in cross-sectional area along the tube). The amount of power needed to produce a clean output depends both on the frequency (wavelength) generated and the shape of the bell. The bell acts as an impedance-matching device to allow the physical pressure wave in the tube to disperse into free space with as little loss, diffraction, back-pressure as possible.
Some examples: a straight trumpet sounds the same (sans valves) as a modern trumpet bent into a double ellipse. Some small radios/CD players have a very long, very convoluted, internal path from driver to exit port to enhance production of low-frequency notes. This path does not significantly degrade the source waveform.