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It occurs to me that the glue between the bottom of the box and the bottom of the aquarium might be treated as a viscous fluid. Even if the glue does seal the box to the aquarium so that no water can seep between them, as the aquarium is filled with water the pressure at the bottom of the aquarium rises, and this pressure might then be expected to squish the glue around the edges, in turn raising the internal pressure inside the thin layer of glue itself, and being communicated to the bottom of the box, despite our best efforts to prevent this from happening. If this were to occur, the box would effectively again have a buoyancy force.
Of course, if you insist on "ideal glue", like massless strings and perfectly rigid rods, .... :-)
Easy to do the experiment: just put a hook in the top of the box (or pole, as some have said) and tie it to a force sensor overhead, arranging things so there is some tension in the string (which is recorded by the force sensor). Now add water. If the glue is communicating a buoyancy force to the box/pole, the tension in the string should decrease.