I feel like I'm at a kids' birthday party, watching "pin the tail on the donkey" and everyone is sticking the tail on the donkey's face or back. Close but no cigar.
Whether it is tape, digital, Leslie, analog or rubber bands and masking tape makes little difference. The key consideration is what makes something *sound* like two distinct individuals doing the same thing. Chorus pedals have historically been an attempt to simulate the sound of....well, a chorus...several individuals singing/playing the same material in synchrony, or at least attempted synchrony. One copy of the signal "takes the lead" and a second copy falls behind and catches up in periodic fashion. You can achieve that by slowing down an analog sample via a bbd, a digital sample, or by twiddling the motor speed control on the tape deck. Hell, if you wanted to, you could start two turntables off with the same track and twiddle the turntable speed control in the corner and do it too.
Is that enough? Not really. One needs to keep in mind what the human ear is able to derive and what its attention is drawn to as the stagger between multiple versions changes. If the stagger is very close, what is noticed is the notches/cancellations created by two versions of the same content closely spaced in time. That's flanging. If the stagger is slightly larger/longer, perception of the notches declines and perception of pitch deviations tends to dominate, as well as an audible asynchrony. That's chorus.
What people generally refer to a "automatic double-tracking" is a similar kind of stagger but somewhat longer, probably more in the 20msec+ range. How is this different, and how is it different than slapback? Easy part first. With slapback, the amount of stagger never changes, whereas with double-tracking it does. The second voice is always discernible as a repeat with slapback. Now the harder part. With ADT, the stagger will occasionally (more in a second) get shorter such that it doesn't *always* sound like a discernible repeat. But will the stagger be, or more importantly
should it be, periodic like an LFO-based chorus? I think the answer can be found by imagining yourself as a singer in a studio trying to repeat on playback what you just sang and recorded. You listen through headphones (put on your best pensive look with hands clasping the headphones, kiddies, and crowd that spit barrier in front of the Neumann U47) and try to remember what you just did to the best of your ability. How accurate will your pacing be? In other words, as you try to recreate the parsing of words, the emphasis, the periods of silence, etc, what will your margin of error be? Likely you will occasionally sing the same thing at almost the same time as the first track, but more often than not, you will be in the vicinity of 25-50msec off, simply because of reaction time, and relative accuracy in preparing movements/actions. The end result will sound like two individuals because of that asynchrony, but here's the big magic difference in my view:
the pitch deviation will be negligible because the stagger will be a function of the duration of silences or sustain of a note, NOT because of a graduated catching up and slowing down as in the case of a chorus.
It IS possible to get close to mimicking this with a sampled-delay (analog or digital). I have one of those old blue rackmount MXR digital delays, and the LFO modulation can be applied to any of its 8 delay ranges. Fortunately, because digital delays of that era had limited delay-modulation (the MXR swept over a maximum 4:1 range), it was easy with that unit to set it for, say, sweep between 30 and 40msec delay. The sound is one I like to describe as being a bit like Pat Metheny, which is chorus-like but has a different ethereal quality that comes from the easily discernible stagger between wet and dry. I haven't heard the "bounce" function on the old Eventide delays that Steve Giles is fond of, but I imagine that might introduce an element of realism too, and is possibly what distinguishes tape-based ADT from totally electronic attempts.
Ideally, though, an ADT would have only the faintest pitch modulation, and would probably use time compression to vary the duration of the gaps between notes. That is probably not the sort of thing you can do in real time, but is consigned to the realm of post-production. Choruses, of course, are kind of stuck when it comes to doing such things, because they have to always speed up the sample output of the audio to catch up and slow it down to lag. While this will shorten and lengthen the gaps between notes, it will also distort the pitch as well.
For the time being, though, and for the adventurous, simply double the clock capacitor on your chorus pedal, to shift the range over. You can easily tack a second parallel cap on the copper side of the PCB for a brief experiment. You will notice two things immediately. That whining. Please, God, stop that whining!! It's driving me INSANE!!!

The other thing you'll notice is that your depth control will need to be turned way down and may not even have the degree of sensitivity needed to dial in just a touch of modulation. These two phenomena result from a) the clock frequency being much lower than the lowpass filtering can filter out, so much more audible, and b) the perceptibility of pitch changes at different delay ranges (flanging changes pitch too, but you don't really notice it because at that delay range it is minimal; longer delays = more pitch deviation).