No. Regular yogurt, while creamy and custardy straight from the refrigerator, can quickly turn icy and hard when placed in the freezer. It has a higher water content than you might think, making it easy to form ice crystals in the freezer.
You can try draining the water from the yogurt by hanging it in a cheese cloth overnight then adding some cream to level out the consistency. You can also add whole milk, cream or sugar to the yogurt to help get the right kind of creamy texture when you take it out of the freezer, but it still won’t be the exact texture of typical frozen yogurt.