Why would you expect a Disney Cast Member to recognize your acronym for something?
In the first place, Disney only used the term "Advanced Dining Reservation" for a very brief period of time. Now they just use "Reservations" or "Dining Reservations" so the abbreviation ADR would most likely elicit a "huh?" from most Cast Members.
Secondly, do you really think that the Cast Members who book dining care enough about the Disney-Obsessed poplulation that frequents these boards to take the time to learn all the different acronyms and abbreviations? As much as people would like to believe that these boards are the pinnacle of Disney information, the reality is that only a very small percentage of WDW guests frequent these boards with any regularity. Plus, when you get out of work, do you spend your free time surfing the internet about your employer?
Finally, Disney has plenty of its own acronyms and abbreviations to keep up with, and as anyone who as worked in a call center will tell you, when you are talking to customers (guests in the case of WDW) you NEVER EVER use the internal acronyms or abbreviations. Instead you use the correct names, such as "Cinderella's Royal Table" and not "Cindys" or "Disney's Polynesian Resort" and not "The Poly."