Are the spouses considered married in the sight of God if they concluded the marriage contract in a Sharia court but did not hold a wedding ceremony, even though all their acquaintances are officially aware of their marriage?

If the marriage contract is concluded according to the Sharia conditions, then it is permissible for the spouses to sit, talk, and be in seclusion with complete freedom. And it becomes lawful for the husband what is lawful for him from his wife whom he has entered into, such as looking, kissing, being in seclusion, traveling, and intercourse.