hmm, I think you could do that (run it through the side) - it would definitely save you some room. Since you are fabricating the sump, this is a good idea.
I think the sock is a nice to have, but certainly not a requirement.
I would just try running it with a fuge and see what happens. I don't have an algae scrubber, just a small fuge growing chaeto, and my nitrate has never tested above 0 ppm
(and I have the higher resolution RS Pro test kit). Remember, if you run a scrubber, you somehow have to fit 2 lights in on either side. I just think it would be really tight fit in that space. If you can work it out though, more power to you.
EDIT: And my nitrate isn't for lack of nutrients - I feed like crazy. The chaeto just grows like mad. It doubles about every 2 weeks. There is not a spec of algae besides coralline and some diatoms in the DT.