I'm going to assume the half-nuts stay closed?
...It doesn't make any difference to the repeatability of re-engagement if the dog clutch is located directly on the drive end of the leadscew(like the harrison lathes) or if it is located on the input end of the drive shaft for the screwcutting gearbox. ,
I'm going to disagree, lathes with single-tooth clutches (Holbrook, Hendey, Hardiinge, Pratt & Whitney - toolroom lathes) run them at spindle speed before driving the QCGB, not leadscrew speed after - at spindle speed it preserves the relationship between spindle and leadscrew (it can only engage once per spindle rotation so once per threading pitch as the half-nuts stay closed), a single-tooth clutch on the leadscrew can engage at any *leadscrew* pitch, with the spindle in an arbitrary position depending on the QCGB ratio, not the same thing! It MIGHT work for "native" threads, as suggested, as you'd effectively be opening the halfnuts and closing them on a random point on the leadscrew, definitely doesn't for anything else, e.g. metric on an Imperial lathe and vice-versa, which the spindle-speed dog clutch will do.
a single point dog clutch will always re-engage the leadscrew at exactly the same relevant index as it was disengaged from and there will be no variation in the relationship of gear engagement because they haven't been disengaged or had their relative timing disrupted.
Except that the spindle can rotate though an angle dictated by the QCGB setting and align the dog clutch without coming to the same angular relationship between spindle and leadscrew - e.g. for the 8tpi leadscrew, 11 tpi thread to cut, the spindle will have rotated 11/8ths of a turn (or multiples of) before it realigns the dogs. Assume the carriage is exactly where the dogs disengaged, the spindle will have rotated an extra 3/8ths of a turn and you'll be cutting a multi-start thread by accident...
I've looked into this a bit, as my lathe would very much like a single-tooth clutch, leadscrew/feedscrew reverse, threading stop and extra control rod, for cutting metric threads among others - added to the complication on my lathe, although the forward/reverse (R/H Vs L/H) selection runs at "spindle gear" speed is that the back-gear drives the spindle at 1/8th the speed of the "spindle gear" (on a concentric sleeve with its own bearings) that operates the QCGB etc. to get the "coarse" threads that really could use a threading stop disengaging a single-tooth clutch... Perfect if you need to cut 8-start 2tpi or 16mm pitch threads.
Plans are being made, slowly, fitting it all in is challenging!
There are a couple of single-tooth setups published, one is in Martin Cleeve's "screwcutting in the Lathe" (Workshop Practice series No.3), another in one of the model engineering magazines a couple of years ago, and all run the dog clutch at spindle speed to maintain synchronisation, there are versions for a good selection of hobby lathes.
Probably not what you want to hear, a leadscrew dog clutch would be MUCH simpler!