Special marriage act

No there's no problem at all if any person has not even a valid document to show case his/her conversion status but the proof of religion might be required in some other context. As the Special Marrige Act 1954 specifically governs inter-faith marriage & if marriage has been registered duly under SMA,1954 no proof is required afterwards regarding the religious status of both of the spouses.It has no effect on the legal nature of the marrige. Though there's no proper solid definition has been given that Who can be called as a Hindu but Sec-02 of HMA mention some specific conditions & says that any person to whom Hindu law is applicable is called as a Hindu . As per it any person who's Hindu By Birth , Hindu By religion , Hindu by Conversion , one of parent if hindu , or if both parent are Hindu. Hence under section 2 of HMA has solidified that if a person was previously a Christian & has converted to Hindu then he/she is known as a Hindu by Conversion. So if a person is a Christian by birth but has started following Hinduism then he/she becomes a Hindu by practice of the rituals & conducts.

In Perumal Nadar vs. ponnuswami Nadar 1970 , the Apex court has held that no formal ceremony of purification or expiation is necessary to effectuate the conversion to Hinduism & all that's is required is the intention of the concerned person to convert to Hinduism or live as a Hindu .

In Mohan Das Vs. Dev Sam Board 1975 it was held that when there's a bona fide acceptance of religion & acceptance of Vedas with reverance,then the conversion is deemed successful to Hinduism.