It can be done. The most logical thing to do, since the bin probably cost you less than your aquarium, is to drill holes for bulkheads into your bin - one where the water will be pumped in from the tank below it, the other at the water level you want for the refugium (so the water will drain back into the tank) - and then install the bulkheads (and associated tubing) in those holes. Keep in mind that plastic storage bins are not intended to hold water and tend to bow when more than half full; this can partially be fixed by keeping the lid attached to the bin and just cutting a hole or two into the lid so you can access its interior for maintenance, though even then you would be best not filling the bin to the brim.
EDIT: I find that, at least with air line tubing (3/16 of an inch ID), you can make an air (and water) tight seal by simply drilling a hole slightly smaller than the outside of the tubing and then pulling the tubing through it (best done by cutting the tubing at an angle, pulling the cut end through the hole, and then using needle nose pliers to pull the rest of the tubing through). I have not yet tested this with larger tubing sizes, though...I really should get a cheap storage bin one of these days and try it out.