I've not had much luck with ADT plugins in the past. Too much "artificial" in the output, and they don't sound at all like real double-tracking.
 
I've been meaning to try an experiment, which could theoretically come closer to the real thing: use two tape delay plugins in parallel. Any tape delay that has pitch modulation should be able to pull it off. I'm thinking the new Imperial Delay might do the trick, or the Tritik delay, or maybe Timeless2, all of which feature pitch modulation (although Timeless doesn't give much control over it). The idea is to just use the wow and flutter feature without much actual delay, simulating the old school method of running the signal through two tape machines and modulating the vari-speed.

Let us know how your experiment goes.  In my very short trial with the Abbey Road Reel ADT, it sounded fairly authentic but I need to work with it a bit more.  I almost never like default settings on anything.
 
I can get decent results with my TC Helicon Voice Works+ but you can hear glitches sometimes.
 
So far, I have been actually doubling voices by singing them twice and making a few Melodyne tweaks, if needed.  I will be interested to see how well Reel ADT works because it could save a lot of time and work (which was Lennon's/Townsend's motivation originally).