Hoosier: I figured you had probably thought it through - you know the construction pretty well
It would be a "hassle" getting the bike in and out, and it would take up a lot of space. But..... if recumbent biking was a big part of my life, I loved my (undoubtedly expensive) bike, and I was solo -- I'd very likely also consider carrying it inside on the dining side. Stays clean and out of the weather, much less likely to be stolen, etc. Plus I'd likely enjoy looking at it (kinda like a surfboard slung on the wall looks good). Plenty of people are "hang out on the couch" types anyway (vs. needing a club lounge). Table pedestal (or Lagun type table) in the aisle and you'd have that space too.
Definitely not going to be un-noticable, but I think it's a good idea to contemplate.