I remember something like this was used in Cryptonomicon. It's been almost two decades since I read it, but IIRC it was a phone conversation between Churchill and FDR that was secured with twin one-time-pads encoded on vinyl records.
If it was a real A to D with digital encryption, it would have needed far more tubes. The digital side would have had to be all electronic. It wasn't. Look at the picture. That's an Enigma mechanism with a very few tubes out back.
Something like that would have sync problems. Not clear what they used as a time base for the demo device. Maybe for demo purposes they just used the power line as a clock.
Before SIGSALY, there was a pre-war Western Electric system, the A-3 [1], used for transatlantic phone calls. That had only five channels, advanced the key only every 15-20 seconds, and only had six channel-swapping patterns. The A-3 was a very low grade encryption system, and was broken by the Germans.
SIGSALY was the A-3 concept scaled up. More channels, faster key changes, additional analog processing. It filtered analog voice into ten channels, and swapped the channels around based on a one-time key stored on phonograph records. This seems to have taken way too much hardware. But it had redundancy, each direction was separate, and there was a pseudorandom key generator for testing without using up one-time keying material, all of which added bulk.
Audio speed analog to digital converters were invented in 1937 by Alec Reeves.[2] But they were not used until after WWII. A usable voice-speed A to D seems to have been beyond the capabilities of WWII electronics. Reeves had the basic concept - a counter, a ramp generator, and a comparator. All of those were very hard to do in 1937.
Reeves is an obscure figure. He invented pulse-code modulation as well as the A to D converter. He spent WWII working on aircraft navigation systems rather than encryption. If he'd been involved in encryption, high-security WWII voice encryption probably would have been all-digital. After the war, he was involved in the beginnings of fiber optic links, so he did quite a bit.
[1] http://chris-intel-corner.blogspot.com/2012/02/intercepted-c...
The 7-tube "combiner" is clearly analog. The key generator seems to be three multivibrators phase-locked with relatively prime ratios. That's cute. It's a pseudo-congruential random number generator in the analog domain.
This exploits the effect that oscillators that are weakly linked will tend to come into sync. Not necessarily at 1:1; you can sync at various ratios, with difficulty. Must have been a pain to get to work reliably. I'd like to see the schematics.
With phase-locked loops and counters this would be easy; that's how modern radio tuners work. Not easy to make reliable with 1940s technology. Getting things to sync up was a huge headache until the 1970s.
[1] https://www.hmgcc.gov.uk/news/turing-s-rebuilt-delilah-machi...