Bearing in mind that it's now twenty-four years since EGG was released, could it be that New Order themselves are slightly confused as to how the pulsing synth riffs on it were achieved?
The FAQ here states:
The first drum machine we had was a Boss Dr. Rhythm. It was all plugging little mini jacks into mini jacks. It was all CV and gate.
He's referring to a Boss Dr. Rhythm DR-55, probably the first affordable drum machine to be totally programmable (as opposed to preset/semi-programmable). It had three sounds. I know this because I owned one too! It was a small jobbie, about the size of a book or something, had one mono output, was battery powered and didn't synchronise to anything.
It's this that can be heard on the intro to EGG and the outro as well and it's also on Truth on Movement. It did feature two 'trigger' outputs with which to run external sequencers (like a Roland CSQ-100 or that of a Roland SH-101) and to trigger other synths. I reckon it's this that's running their ARP and they admitted as much on the Music Technology interview from 1985, saying they "pulsed the individual sections to get that sequencer-like effect and then layered the strings over it".
They said then that this is the method used on Temptation and the second Peel session on tracks like 586 with the Powertran sequencer (which Barney built from a kit) but which Steve described as "mickey mouse". This setup was ditched in favour of the even more unreliable Prophet V/Polysequencer setup used on P, C and L and Low-Life.
The difference is that on TX: New Order a couple of years back, they tell a different tale, saying Hannett had this idea that they could pulse the ARP using the VU meter from Steve's hi-hat. They even said it worked! It might've worked at the time but Steve doesn't play sixteenths closed hi-hat throughout the track (unless he did and it was mixed out later) so I personally think the beatbox method is a lot more likely!
Happy for this to be placed in the FAQ if the fine moderating chaps here feel it's not greatly relevent.
Ps The Yamaha QX1 sequencer was a massive and labyrynthine beast that "took three hours to get going" according to Hooky. They used to use it live!