Yes. Probably immediately and violently if the capacitor was used as a low-pass filter or a similar configuration. If the capacitor was used in a high-pass filter (or similar), then the damage might take some time to appear (if at all), and it might not be as violent.
what could go wrong
If it was a low-pass filter or similar, then expect other components to overheat quickly. Depending on what type of component dies first, you might be lucky and just get a light-emitting resistor. If however an electrolytic capacitor dies first, then you'll probably have to deal with a lot of nasty smelling smoke, that might take days to get rid of. Also, overheating electrolytic capacitors can explode if you are unlucky enough, what might do physical damage to the circuit board, or even the casing or panel.