You could certainly use Allegro to make an ASCII game. There's an alternative library called
libtcod, which was specifically designed for ASCII games (well, roguelikes, but you can use it for anything). It's built on top of SDL with an optional OpenGL-based renderer. If you were to make an ASCII game with Allegro, you'd likely be implementing many of the same features yourself. For example, libtcod allows you to work with a virtual console buffer, a rather convenient way of handling an ASCII game. In Allegro, you'd either have to implement that on top of the bitmap API, or just work with the bitmap and text API directly. Personally, I'd go with libtcod.