Praise be to Allah.
If the marriage contract to which you refer fulfilled all the necessary conditions and included the proposal and acceptance, in the presence of the woman’s wali (guardian) and two witnesses, with the woman’s consent, then it is a valid marriage with all that that entails, and the woman has become your wife thereby, even if it has not been announced and publicized and even if it has not been recorded officially, because the Prophet (peace and blessings of Allaah be upon him) said: “There is no marriage except with a wali (guardian).” Narrate by Abu Dawood (2085), al-Tirmidhi (1101) and Ibn Majaah (1881) from Abu Moosa al-Ash’ari; classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
And he (peace and blessings of Allaah be upon him) said: “There is no marriage except with a guardian and two witnesses of good character.” Narrated by al-Bayhaqi from ‘Imraan and ‘Aa’ishah; classed as saheeh by al-Albaani in Saheeh al-Jaami’ (7557).
Having the marriage documented in the court and so on is not a condition of the marriage being valid, rather it is done to protect people’s rights, and hence it is essential. But it does not matter if that is delayed until you obtain the divorce documents.
We ask Allaah to bless you and to bring you both together in goodness. We advise you to fear Allaah and treat your wife kindly, and to establish a righteous Muslim household.
And Allaah knows best.