To me, a big part of the "fretless thing" comes from a rigid, strong neck with a hard fingerboard and a solid body. Deviating from this will generally reduce sustain (give a more "thumpy" sound), make the sound less clear and defined (turn more "warm"/"wooly") and reduce upper harmonics (make it sound "bassier").
Since I personally find most use for a fretless in slow, melodic songs and playing small "counter phrases" (word?), I want good sustain, clear pitch and good mids.
For a more traditional "upright" feel, the fretless acoustic bass guitar might work OK, though. For more modern music, I'd pass.