Just as
@Newmarket said, transformers don't pass DC through to the output - that's not the issue here. The issue is that the DC will flow through the primary coil to ground, which will likely cause distortion, and in some extreme cases, can burn out the winding (they are often low DCR and low wattage ratings because the wire is so thin). Let's say you had 2V of DC offset (an extreme example), and the primary DCR was 10ohms - that's 200mA of current at 2V, or 0.4W. If the magnet wire used in the transformer is only good to 1/4W, you may burn out the coil.