IIRC, we arrived at the check in desk around 4 PM and they open for checking in around 4:30. We asked if they were taking walk ups and the CM said they would be having a meeting soon to see if they would take any. She said to be back at 4:30. By that time a line had formed behind us so we decided to camp out until the CMs returned to start checking people in. Meanwhile, I kept checking on my phone to see if any reservations popped up. About 5 minutes later I managed to snag a 5:20 reservation on my phone, so I dropped out of line and my wife stayed to check in with our new reservation. Since the reservation was brand new, they actually needed the confirmation number to retrieve it. My wife got us checked in and we sat in the bar waiting for our buzzer to go off.
Now, to answer your question, the people who got in line right behind us we also looking to do a walk up. My wife noticed that at least one party was seated ahead of us and we were probably seated around 5:15. This was on a Saturday in early February.
We also went on the Monday before, arriving with reservations, and noticed that they were taking walk ups that day too. One of the walk up parties was still waiting to be seated as we were leaving, which was probably around 6:20 or so.
So, yes, it is possible to do a walk up, but it is also probably best to arrive before they start checking in to ensure you get your name in first. It also never hurts to keep checking the online reservation site to see if something opens up. During some of my random checks during the week we were there, I even saw a 6:00 Le Cellier show up.
I believe 'Ohana is our new favorite place to eat in the World, I can't believe we waited so long to try it. Now, if only Le Cellier would start selling their Pretzel Sticks at a stand outside...
. I would keep checking online everyday before you get there, and then I'd keep trying while you're there 
. If you aren't able to secure an ADR, it can't hurt to walk up.....you never know what might happen 
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