It sure does!

Thanks to the awesome group over at: https://archon.im/arianet/matrix-homeserver/services/ !

From their document:
The address syntax to access XMPP from Matrix:

• Private chats: @_bifrost_USER=40DOMAIN:aria-net.org
• MUCs: #_bifrost_MUCNAME_MUCDOMAIN:aria-net.org

You can start new matrix chat from the Beeper Desktop Client by going to the compose icon > Create New Beeper (matrix) chat, for new private chats. Article here.

You can join a matrix room from the Beeper Desktop Client by going to the gears icon > Join Matrix Room

Note: Make sure to change the matrix room server to whatever aria-net.org: