To start with, I wouldn't take a Wikipedia article as any sort of gospel truth. A lot of them are "works in progress," to put it kindly. That Wiki article implies that a singer can do a true double-track that's within a few milliseconds of the timing of the original track, which I find very hard to believe.
Anyway, ADT doesn't use delays of only a few milliseconds -- that's down in the flanging range, and ADT is not flanging or static comb filtering, it's more like somewhere between thick chorusing and a short slapback delay, although there is no "official" definition of what delay range is ADT. I'd guesstimate 25-75 ms as being the ADT range; 100 ms is starting to get into short echo territory. I would imagine that they had to run tape machines at fairly high speeds, or use ones that had very little space between the record and playback heads, to get those delays.
Remember the old MXR rack mount Flanger/Doubler? The Doubler mode is an example of what I think of as an ADT effect. The old Electro-Harmonix Full Double Tracking effect had a choice of two fixed delays, 50 or 100 ms if I recall correctly. Adding some modulation makes the double-tracking less fake sounding, but it has to be very, very subtle, or it will just sound out of tune. You want something on the order of the wow and flutter of a good tape deck, not something that will make you seasick.
btw, the "warbly" sound on Beatles recordings was usually a Leslie, right?
