There is "some" sidespill from those type optics, keeping in mind that you have around 90%+ efficiency from acrylic (typical rating) lenses, and of the rest, some of it is lost "in" the acrylic (absorption), the actual "spill" out of the lens is probably less than 5%.
Of that, (nice design, by the way), only a small fraction would have an incident angle allowing it to "exit" your side lens, maybe 1-2% of the total lumens, over a 360* dispersion, so not a lot. I'd recommend if doing something like this, to "frost" the lens (rough the exterior if acrylic) turning it more into a "marker" light than a transmission light, because not much will project out (and what does, would be a very faint "halo" on the surroundings, rather than a smooth flood lighting up the area).
Anyhow, just my $0.02, I've tested similar ideas in-house (a variety of lenses), and in all cases, it's best as a weak marker (or even "on-indicator" of sorts), rather than any useful area lighting.