If you don't remove the algae, you don't remove nutrients. If you don't clean the screen every 7-14 days, the bottom layers of algae will die and put nutrients back into the water.
What kind of glue would you suggest that is aquarium safe?If space is the problem, I'd wait and do the new design, which requires no sump. But yes the bucket will work if you line it with glued-on canvas. Just roughing it up will not be enough, however... the algae will let go when thick.
I'll post a link when the new DIY is ready.