No, Ariana has no scheduled flights out of Dublin. However, Ariana does fly out of Istanbul. There are also other airline options to choose from if you still want to book a flight from Dublin. Air Algerie, for example, is an airline that flies out of Dublin on a regular basis.
Mazar-I-Sharif is the most popular airport that Ariana serves, followed by Kabul Khwaja Rawash and Herat.