Hi Dan and welcome. The B7 is certainly designed for Gibson ES 335-style guitars (the guitar the
ES-1GT is based on), so that's a good start. The kits certainly have a solid centre block that runs quite a way back, though I don't know if it it runs all the way back the to tail end. As far as I can make out, the original construction varied with Gibson through the years. Some had a centre block that ran all the way from neck to tail, and others had blocks that ran back to a bit beyond the stop tailpiece. I've got a feeling the kit is rather like the latter, as it takes less time and effort to profile the block to the curve of the top.
The B7 tension bar sits a lot further back than the stop tail on a standard 335, so if it is a 2/3 long block type, the locating screws will probably just be running through the ply top. However, I don't think the screws do too much more than help locate the trem, and there should be enough strength in the top to support the downward pressure, as the B7 can be used on fully-hollow archtops as well.
If you don't want to risk it, there is this adapter plate you can get
http://www.vibramate.com/vibramate-v7-335-install.php that is designed to fit on a standard 335 and uses the stop tail piece stud holes to fit a B7 without the need for any extra hole drilling in the top. It's more cost, plus there's no guarantee that the kit size dimensions are exactly the same as a real 335. Also the kit hardware uses metric sized stud holes and screws, and it might require replacing the studs with true Gibson-sized ones to make it all fit. However, it does give your son the option of removing the Bigsby at a later date if he then prefers a non-trem guitar without leaving screw holes in the top that need filling.
If you do decide to get a kit and add the Bigbsy, I'd suggest getting a replacement roller bridge, which does a lot to help keep the guitar in tune.
A lot of conjecture there, but I just don't know. For a definite answer, email Adam Boyle, the PBG owner, and he should be able to give or get you the full answer (details at the bottom of the PBG home page).