No you can't receive Holy Unction if you arent Orthodox Christian, if your really sick maybe you can ask father in your situation, most likely ask him before the service. However if there is Anointing at your parish, you can receive Anointing, which in itself is a blessing.
BTW it begs the question , I am about to go to Confession for Holy Unction , I didn't keep a whole 6 hour fast, father kinda hinted we need a Tiny bit food, and fast as long as possible, should I still receive, and is there more than just confession and fasting needed? Almost 3 years in, and still have to ask these questions ::embarassed:
Anyways, it seems the order of the Holy Wednesday service is different for each church, and jurisdiction, I learn something new all the time in Orthodoxy. In my parish we had the presanctified liturgy at 8:30am, Holy Unction is at 4pm, then Matins and anointing is at 7 pm, Holy week really picks up on Wednesday.