Charlie: Bigamy without obtaining a state marriage license is virtually never prosecuted unless there are additional serious crimes involved such as child abuse. This is clearly evidenced by the Fundamentalist Mormons in multiple states openly practicing polygamy for the last over hundred years in the U.S. The few sporadic attempts to prosecute fell apart and the attorney generals of those states today do not involve themselves indicting on the states archaic, unconstitutional and unenforceable anti-polygamy laws.
And it is absolutely legal for a mesader kedushin to not involve himself in filing a civil marriage. And very many are mesader and don’t deal with the civil marriage license or regulations. If there are any antiquated unconstitutional laws from a century ago saying otherwise, they’ve been rendered unenforceable by many court decisions since, not the least being the SCOTUS toeiva ruling.