Can a display landline phone instrument be made to work without a separate electrical connection
I don't see any problems with your assumptions in the first two paragraphs. I can't think of a technical reason phones couldn't be designed to provide basic functionality in the case of power loss. It would save having a seperate phone for emergency use during power outages and I'd expect it wouldn't cost more than a few dollars extra to implement.

However modifying an existing phone is not likely to be practical. You'd be working 'blind' without a schematic and reverse-engineering high-volume designs that are likely to contain some custom / programmable chips without design information or source code is likely to be difficult. 

I don't believe you'll find an easy solution for modifying one. Unlike a "simple" phone for example the DTMF (touch-tone) generation is likely connected to all the same circuitry that powers the other functions so trying to isolate the core functions from the more advanced without documentation would be tricky.