I do not recall ever being offered specials at any Epcot restaurants. Our TS dining experiences include Le Cellier, Chefs de France and Restaurant Marakesh in Morrocco.
What was different, however, was that the menus published online did not include everything that the restaurant offered. For example, in France there were quite a few additional desserts that were not listed on any published menus.
I think that menus that include fresh fish might be more likely to offer specials based on market availability and freshness.
There used to be discount specials. I don't remember the details very well, but I think it was eat TS for lunch and get a coupon for a discount on TS for dinner. However, that was so long ago I don't remember the details!
We've been to quite a few that had "specials" which weren't on the menu..Le Cellier, Rose and Crown....they weren't any cheaper if that's what you are looking for but were different offerings.
Not so much looking for lesser prices...just more variety. For those who have eaten at LaCellier...how big are the appetizers? Large enough for two people to share them? What's good?