Dipoles aren't always directional but you get a forward and backward.
True.
But assuming a flat baffle, the directionality arises because the baffle separates the frontwave and backwave such that they meet, out-of-phase, at the baffle's edges. So there is a plane of cancellation (and partial cancellation as we near the plane) which causes the directionality.
If the baffle is folded straight back, I think the plane of cancellation is halfway between the outwide wrap-around distance and the inside path distance. I think this halfway point is not quite all the way back because the outside path length is longer than the inside path length. Thus the plane of cancellation is not quite all the way back.
Now if the baffle is folded into a two-fold dipole (reverse tapered in this case)... hmm, now it's no longer clear to me. I'm not sure where the plane of cancellation ends up, or if it even it's still a plane. The outside path length to the opening (woofer face to horn mouth) is much, much less than the inside path length to the opening so... is the plane of cancellation now inside the box? But inside the box, the SPL from the backwave will be much, much louder than the SPL from the frontwave energy which makes it into the opening, so I don't think there would be much if any cancellation there.
Anyway I
think the net result is no significant directivity, as there would be with a "normal" dipole... just progressively greater cancellation (at least south of the 1/4 wavelength path length frequency)... but if I'm missing just one little point along the way here I could be completely wrong.