Have they been out and diagnosed the fault?.
If you switch it off engineer will not be able to see it in it's fault state which could hinder repair HOWEVER some parts can't be accessed if in solid ice.I carry a hairdryer to quickly defrost areas but some engineer walk away,order parts and arrange to come back another day!
Back to your question.In a warm room and with all fridge/freezer doors open it should defrost within 24hrs
CK, November 2013