I sometimes use TB 2 for outside work that is not subject to puddles. Bird houses should be fine with TB2 - I have even made cutting boards with TB Original, without problem - just don't let them soak. I worry about any glue on outdoor furniture where a puddle may form, such as in the seat of a chair.
I, too, love PL Urethane construction - far better than Gorilla glue. I don't count on gap filling, though, since the foam that fills the gap is not very strong. The spout in the glue tube seems to plug quickly, so I then punch a small hole in the calking tube, near the spout end, and use the remainder from that part of the tube - a new hole each time I need some. I just rebuilt an exterior door, and when I was done, there were some small hollow areas that I filled with PL glue, counting on it expanding to keep water out.