They could if the TUI had runtime/library designed for it.
Emacs as a platform is a good example here - the TUI that you can achieve in it is similar to web GUIs made of standard components - in the the UI isn't just pixels on a 256-bit canvas, but it's made of building blocks that you can inspect, select, copy, and that gracefully enhance/degrade when you switch between graphical and terminal modes.
That might be true for more minimal TUIs, but I don't think most screen-readers can handle the multi-paneled ones like OP.