Obvious caveat: the BFS isn't completely real right now, and what The Public knows about it is even less limited than whatever has been finalized in the design. I guess what I'm saying is some of this might sound stupid, but I claim that's not my fault.
Based on what we know about the ITS per the video on it, the BFS will be vertically integrated on the BFR by picking it up by the nose with a crane. So yes, the BFS can apparently handle being in tension under 1 gravity. (The same crane is in the BFS video, so I haven't seen any indication that the vertical integration plans have changed).
I'll even go one further and say that I'm not aware of any rules of thumb that would indicate otherwise for aerospace structures. Metal structures in general do okay under both tension and compression; composites depend more on the specific layup I think. Even if the structure doesn't do equally well, I'd expect the G loads going up to be 3 or more axial G, so 1 or less G in tension doesn't seem unreasonable.
If that wasn't true, you're already doing non-trivial modifications to the ship, so in your scenario there's no reason to believe you couldn't reinforce the structure somehow.
Essentially all we know about the BFS is that it's designed to be a reusable spacecraft. SpaceX's ambition is to be able to use them in place of airliners, among other things. You're talking about sacrificing a revenue-generating asset.
I don't think that we can reasonably believe that there will both BE a BFS as envisioned by SpaceX, and that it would be cheaper to disable it and leave it in space instead of having it deploy the same amount of volume and support systems as cargo.
To generalize, I'm not aware of any wet workshops being envisioned for something that was already intended to be reused. All the ones I'd ever heard of were attempts to recycle tanks/stages that would otherwise go to waste.