In renovating a basement, is it possible to install a solar-light-tube through the wall to the outside and still gather light?
I'm assuming you need at least one bend to do this? Otherwise you could just put in a window. Adding bends significantly decreases light transmission. The inlet also needs an open view of the sky for maximum light gathering. An inlet on or next to a wall cuts access at least in half, possibly more depending on orientation.
You could run it up to the roof just like a chimney, but added length also diminishes light transmission. These tubes are best with fairly straight, short runs. Complex installations are just not worth it. From what I've seen, even with simple installations, the transmitted light is only decent on bright sunny days. It's relatively weak otherwise.
In the end, the precise details of your installation would determine if this is practical. The manufacturer has recommended maximum bends and lengths in their installation instructions, based on a roof top inlet. The maximums should be reduced significantly for wall installations.
Will the tube be straight? Are you running the tube above the foundation and sill and under the floor joists? So the tube is sneaking just over the outside foundation?
If so, it will be like a round window and gather some light. If you put it on a sunny wall it will bring in good light, especially when the sun hits it.
I put one on the north side of my roof in an attic. Even without direct sunlight it brings in a lot of light.