I guess this is a 5-speed derailleur Sprite rather than the S5 Sprite. I'm not sure why the pictures of the bike won't show up on my computer, but my fault if I've got the wrong Sprite.
On the 5-speed hub, yes- they had a concept down early on. I first learned that when I got Tony Hadland's excellent Sturmey Archer book and read through it. I was surprised that they were so far advanced in those post-WW1 years. It would have been a huge leap forward in 1922. Even had the S5 come out 30 years later, in 1952, as a follow-on to the FW, that still would have been good progress. By bringing the S5 out so late (along with those fragile plastic shifters and the sheetmetal bell crank), it sort of became a footnote rather than a key piece of what Sturmey was offering and selling.