Yes, that kind of thing.

On a regular non-folding bike, there's usually a way to adjust chain tension on a single speed or IGH hub, whether just horizontal dropouts, eccentric BB, or other mechanical tensioning system. So first off, the Birdy has vertical dropouts at the rear, no adjustment possible. Second, the chain line length changes when folded, so even if you did come up with a "magic ratio" which had the chain in tension enough to be serviceable, it would probably get out of whack when folded.

But again, no reason you couldn't just repurpose your existing derailleur to do the same thing, and it would allow you to keep the chain-catch gizmo as well.