The GG works best with good tight joints, and lots of clamps or screws to hold things tight as it cures. The foaming that fills the gaps, also spread them. You will get the strongest joints if you wet both pieces of wood well, and then let them dry until the surface isn't visibly damp. The polyurethane needs water to cure. The more moisture, the more it foams. Conversely, it will wick deeper into the wood and give a stronger joint, if the water it needs, is in the pores of the wood.
All that said: In your application I would use one of the gun grade, polyurethane construction adhesives. It will give you a well filled joint of considerable strength, more than you will need. This is particularly true if you have joints designed to be glued and screwed.
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