Not so fast,
Well, the RAP-10 is just a general midi board so as long as you get it working as a midi device in your OS then you can set it as an output for DOSbox's midi. My RAP-10 presents itself to DOS as an MPU401 UART so assuming you can find a modern driver for one of those you should be able to make it work, however it would seem the chances of that are slim.
A workaround would be to put the RAP-10 into an old PC and connect that to your new computer over a MIDI cable and use some midi forwarding software on the old PC to route that input to the input of RAP-10.
Currently working on new DOS game, Chuck Jones: Space Cop of the Future : https://chuckjonesdevblog.wordpress.com
WARNING: contains rocket powered El Caminos