It was VERY VERY slow at the parks when we were there last week but at Le Cellier I watched them turn away quite a few walk ins as we waited for our ADR. "Sorry but we're full for the evening." was the standard reply.
Chances of getting in as a walk in are slim but if you can't get an ADR (we booked ours at the earliest booking window to ensure our space!) you would want to TRY and walk in right before opening - and as posted previously, lunch would be a tad easier than dinner. If they open at 11 (not sure if that is the time for their lunch) you should try to be there about 10:30-10:45 to see if there is space.
I was told Sci Fi was full one day (called WDW Dine the day before our ADR - we wanted an earlier res than we had booked) and when I asked about 20 min before opening they were able to get me in. Not that one can compare Sci Fi with Le Cellier... LOL
Good luck! I hope you're able to get an ADR before you go on your trip. Call EVERY day!