Is marriage with the intention of ratifying it later in the Sharia court considered legitimate if agreed upon by a man and a woman who are currently unable to complete it officially due to legal or procedural obstacles?

Marriage has pillars, which are: the woman's guardian or his agent, two just witnesses, a dowry, and a formula indicating the contract. Registration in court is not a condition, but documenting it is preferable to avoid disputes. If the contract is limited to her becoming a wife solely for the purpose of obtaining residency, it is unanimously invalid, and cohabitation is considered adultery. If he marries her without the permission of her guardian, two just witnesses, a dowry, and a formula, the marriage is invalid according to the majority of scholars, but valid according to Abu Hanifa, and it becomes valid and binding by the ruling of a Sharia judge.