How to address a doctoral candidate who is ABD (All but Dissertation)? Is "Dr" appropriate?

Address them the same way you would address any other person without a doctorate: e.g. in many English-speaking cultures, "Mr. Smith", "Ms. Jones", "Mx. Brown", or if you are on friendly terms, by their first name.

If they have successfully defended their dissertation but not actually received the degree, this is a bit of a gray area (see When can you call yourself doctor?) but I think "Dr. Brown" is reasonable.

"ABD" is just silly, IMO, and I'd avoid using it like the plague. To me, it carries nothing but negative connotation.

First, defending a dissertation is too big to be an "all but". It's the culmination of a serious academic experience. I've seen plenty of students get to that point only to have the degree disappear.

Next, the dissertation and the defense is a big step. Not being able to get your act together to write and defend when you're at the "all but" stage is a sign to academics that something is not quite right.

Finally, even if everything is going perfectly, and you've completed the research and writing it up will take the normal amount of time, then using an artificial title makes it look like you're anxious to have a title.

Long story short, when you start, use "Ph.D. student". When you've been advanced to candidacy, use "Ph.D. candidate", because that's what you are. I'll stick my neck out and say that when you've successfully defended and dealt with any corrections and revisions your committee wants handled, but you're just waiting for a ceremony, it might be OK to use Ph.D., but I'd leave it out, and on my CV I'd list Ph.D., with the date defended and the date the degree will be conferred.

Such a person is entitled to be recognized as a "PhD Candidate", which would follow the name and probably mention the department or emphasis ("PhD Candidate in Electrical Engineering" in my case). This might be used in a signature block or a biographical sketch.

There is no special honorific to use antecedent to the name, as Nate has already told you.