Marriage without a guardian is permissible according to the school of thought of Abu Hanifa. This is also the school of thought which does not require the permission of the guardian in marriage on the condition that the husband is suitable enough for the woman, but if he is not, then it is permissible for the guardian to object the marriage and make it invalid.
If the man is suitable enough for the woman, and it is a marriage with the intention of keeping it, and the conditions for marriage have been met, the asking, and accepting and the dowry, then it is an acceptable marriage according to the law in this school of thought, even if it is not documented with official authorities. The lack of documentation does not invalidate the marriage, but it could harm the woman if something happens and the husband denies their marriage, or they have an argument. Because many countries do not listen to the cases of customary marriages, that is not authenticated or documented.
It is recommended that these marriages should be documented and authenticated, even if it is in a country that is not ones. The marriage should be authenticated to ensure the safety of the rights of the woman, and there may be children between them etc.