Would divorcing a wife twice after a new valid contract, when the first marriage contract was invalid and not consummated, be counted as three irrevocable divorces?

For a marriage to be valid, two Muslim witnesses must be present at the عقد (contract). However, some scholars hold that publicizing the marriage suffices, without the necessity of witnesses. If the marriage was publicized and became well-known, it is valid. Nevertheless, it is preferable to renew the contract as a precautionary measure, without the need for a divorce. If a divorce occurred based on the belief that the marriage was invalid, or if it was contingent upon a condition that did not materialize, then the divorce does not take effect. However, if the divorce was for another reason, it takes effect even if the marriage was فاسد (irregular/corrupt) or disputed.