Usually, the answer is yes-it comes out of the total grant award. But, usually there is a travel stipend included in that total grant amount. For instance, i am headed to Poland in August, and they are giving me a monthly stipend, a separate research stipend, and a separate travel stipend for both myself and my wife. Generally speaking the plane ticket must be bought well in advance of the beginning of the grant period, and is reimbursed after your fellowship/ETA placement begins.
Hope this helps.