Yes. But it depends on what class you're booked in.
In general, that is a great idea, I flew with my family on ElAL, then flew on them for free with the miles that we credited to AA, bought Elal "tickets" on AA. If we would have gotten Matmid on the first flights, we would have earned 5 and a half points which expire after a month (exaggeration but you get the idea)