are they married

Salam, when a man SWEARS that he won't have a sexual relationship with his wife for MORE than four months, then that is called Elaa إيلاء‎. If he hadn't had a sexual relationship with his wife more than 4 months, then the wife must go to the court/judge to order the husband with divorce (this is Malek's opinion). Abu haneifa said that the wife is directly divorced when the four months had passed. If the man had a sexual relationship during the 4 months, then the Elaa ends and he must do Kaffara‏ كفارة يمين ‏‎. There must be a sworn oath in the Elaa. If a man hadn't had a sexual relationship with his wife for more than 4 months because he was abroad, then there is no divorce.

Allah says in Surat Al-Baqarah ayah 226 and 227 [2:226-227] [For those who swear not to have sexual relations with their wives is a waiting time of four months, but if they return [to normal relations] - then indeed, Allah is Forgiving and Merciful.. And if they decide on divorce - then indeed, Allah is Hearing and Knowing.]