Properly, no. But there is a workaround, and it's better.

Have your friend call Amtrak (or Amtrak Guest Rewards, if a member) and buy an "open sleeper" ticket. This costs the rail fare (second least expensive coach fare) and allows the passenger to join you--and get meals, because it is a sleeper ticket. (On Amtrak, the first occupant of a room pays the full accommodation cost of the room, and subsequent passengers only pay rail fare. I assume you paid the accommodation charge, else you wouldn't have the roomette. I assume you know that meals are included with sleeper tickets.)

Getting an open sleeper ticket is an unusual situation and your friend might well get an agent who doesn't know how to issue the ticket. Also (at least a few years ago), the ticket cannot be issued as an e-ticket, but only as a paper ticket, and the passenger must pick it up from an agent at a staffed station. (If your friend is boarding in New Orleans, this should not be an issue.)

If you want more information, I can try to find a thread on another web site (Amtrak Unlimited) that discusses this. I have never traveled on an open sleeper ticket, but I have had someone on an open sleeper ticket join me in a room (and get meals).