Sure, just as if I filed a fraudulent property tax form. If you refuse to file a return, you do face criminal sanctions for your refusal to file, but again, you do cannot be compelled to state the nature of your illegal income. By your logic, only criminals would be free from filing a return.
That's similar to the requirement to apply for a social security card in order to work if I am an illegal alien, because to do so would incriminate me. And yes, the BOR does apply to illegals.
It’s all a charade.