I had, in the past, also been thinking a bit about how the system could work offline because it would avoid a lot of security issues for something like a medical office that wants to create content that's then copied into a medical records system.
My initial thought was to bundle a local copy of the server with pre-trained models, but that becomes problematic on mobile clients. I'm writing the server in Go, so if I go that route I'd probably need to reimplement parts of it in another language and avoid using any remote APIs.
So the answer is: very likely yes, but not initially. You've definitely moved the functionality up my planned features list.