In Turkey, you can have a religious wedding ceremony if you want to complement the secular ceremony which makes your wedding official. If the couple is not married officially, then triple talaq can be in force but in official marriages triple or quadruple talaqs would have no force and I think the couple in question is probably officially married.
Even though Turkey is a Muslim country, it has been strictly secular, The current government is trying to islamisize the law and especially civil law but they have not succeeded to do it yet up to now. By the way official name of Turkey is Turkiye now (letter u having two dots, umlauts on top)