Based on the Wikipedia info about screen readers, they seem to prefer text written serially to the screen, such as through the DOS console device. Some text games write to the screen non-serially, possibly writing through INT 10h or directly to video memory, so are not well-suited to screen readers.
Going by your chosen title on vogons, I'm guessing you have Infocom games in mind, and they tend to write serially for the most part. The Z-machine interpreter has native implementations on a wide variety of platforms in open source, so you needn't involve DOSBox for developing a facility for the blind.
One idea for DOSBox and Infocom games is to use the original DOS interpreters running in hal's megabuild with printer support. The SCRIPT command in the original interpreters causes the game text to be written to the printer as well as the screen. The UNSCRIPT command turns off printer output. If screen readers can capture printer output, such a configuration may be workable. However, sending keys from an external application to DOSBox could be complicated, and platform-specific, but there are key macro application that do that, so it may be possible if not exactly easy to do.