Village Education

The Irish National School system, is the system within which most primary (up to 12/13 years old) takes place still. The system is essentially a continuation of the system of education put in place by the British Government in the 1830s. From the begining these were free to all children and still are - more or less, there is a 'voluntary' contribution.

There is a national school in pretty much every village in Ireland and in many rural areas. They do not generally have nuns teaching and never did.

Alongside this system there are primary schools run by religious orders, often private fee paying schools in the past though most are now also free. They would have had at least some nuns teaching in the past, though it would be rare now. However they are more likely to be in large towns and cities, it would be very unusual to have such a school in a village or rural area.

So, basically, the answer is no, but it's not impossible that it happened in the odd place.