firstly, yes you could build a utube out of pvc and both ends would have to stay submerged.
the size of your return pump (GPH) will determine the diameter of pipe you need to use for your u-tube. since its a nano, i think 1/2"-3/4" would be sufficient.
you asked "If the overflow box would empty, wouldn't the siphon stop?"...yes, but the overflow box will not empty if its built properly. to build it properly, you must have a large enough surface area over which the water can flow into the box. again, the size of your return pump will determine how much surface area you need. in a nano, it wont have to be that big. once the water begins to overflow into the box, it will keep a constant water level, usually about 1-3" deep. your u-tube will be submerged below this, ideally 1/2" above the bottom of the overflow box.
all of this is hard to imagine without seeing it first hand. i suggest you build it and try it and if you have specific issues post em