Nitpick: It's not ASCII. It's simple 2D bitmaps. You can't play DF in a character console.
I wouldn't recommend it, because it's noticeably slower than the SDL or OpenGL renderers, but you can.
I don't want to run DF on my local system - I want my DF world running on a server in a rack somewhere and I connect over screen/SSH when I need to.
Is that a sane use-case with recent DF releases ?
A release or two back it gained a true console mode which you can play on a real terminal.