The box is as closed as any closed box above the working range of the pipe (or port).The weakest part is the front baffle with all those cut out holes.
DrBoar, the volume of the box is large (160 liters) and the four drivers displacement is not much (400 cm2 cone together) their is no high presure build up on the panels like in a small sealed box or ported box. The opening and tunnel of the TL is almost as large as the cone surface so their is not much of compresion. The air load on the cone from the collom is relativly low and the force on the the walls of the box is very low. The working range of my TL is 20 - 40 Hz with a 12 dB cutt of at 40 Hz. So their is not much energy above working range. That is one of the huge benefits of a TL compared with sealed or ported boxes with a low cut off < 50 Hz. This is also important to avoid panel resonance and get good integration with the main speakers.
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I finished the saw dust and the results are there, made some tone sweeps and measurments The long sub goes untill about 28 Hz down in my room (15 x 9 feet) without rattels, resonaces or other bas stuff. From 30 Hz up is it's strong point. It's tuned to 30 Hz and i added some stuffing in the back chamber and line to flatten out above 40 Hz. Was only surprised that my electronic cross over at 40 Hz / 12 dB still passed a lot above untill 80 Hz. Maybe in the futere i will get a more steep filter, 24 dB or so.. very satisfied with the TL bass results combined with these small styrofoam woofers. ;-)