Answer: In [an Islamic] marriage, the spousal relationship is established by the verbal expression of the proposition and the acceptance (Nikah 'aqd). More over no action or deed that reflects the intention of marriage can be a substitute for the spoken words. Consequently, the marriage mentioned in the question is not valid except after the pronouncement of the religious marriage formula that does not have any retroactive effect.
As for the children, they will be considered legitimate if the parents did not know the law [requiring the ‘aqd] because their relationship will be classified as “wat’i bis-shubha”. But if both were aware of the law, their relationship is considered adulterous. Consequently the children will be deemed illegitimate. However, if only one knew about the law without the other, the children will be deemed legitimate in relation to the ignorant parent only.
Ayatollah Al-Sayyid Ali Al-Husseini Al-Sistani