I had two ADR's for lunch at Le Cellier last February. On both days, while I was waiting for the restaurant to open, people would come in and ask about walk ins. The hostess told them she wouldn't know until the restaurant opened if they would be taking any walk ups, or how many they could take. On both occasions, they did take a few, because I saw these same families seated not long after I was. I imagine they try to discourage walk ins at Le Cellier, and I also figure they probably handle it on a day by day basis, so it's safer to just say "no walk ins" than to say "well, they may take walk ins if this, that, and something else happens". Fewer disgruntled guests that way, since they know there will be some people inquiring about walk ins regardless.
I would try calling Disney dining the day of, and if that doesn't pan out, it doesn't hurt to ask at the restaurant, but do it for lunch and plan on being there when they open. Be sure you have a backup plan in place to dine somewhere else if you can't get in. Although I enjoy TS dining, I hate scheduling my vacation around ADR's, so I'm OK with CS if a last minute TS doesn't pan out.