Actarus is saying that because it has you doing so much volume, it will promote sarcoplasmic growth, which basically means that it will increase muscle size by filling the muscle with mainly water and glycogen. (This is accomplished by the 15s and 10s with HST.) This is nice and all, but if you want "real" growth, meaning growth in the actual muscle fibers, you'll need to be lifting heavier weights. (This is accomplished by the 5s with HST.) This is known as myofibrillar hypertrophy.
Also, if you stop doing high rep/high volume work, you will lose the size gains that you achieved from it. That's
one reason, but certainly not the only reason, why people will use dropsets during the 5s: to keep their muscles pumped up with fluid and glycogen, since 5 reps is not enough to accomplish this on its own.
While high rep/high volume programs similar to GVT are effective for the pros, they don't work as well for natural trainees.
Based on the SAID principle, GVT should lead to increases in your 10 RM, unless you can't handle the volume and get into overtraining.
For more critiques of GVT, see Bryan's article
Is German Volume Training "Hypertrophy-Specific"?
If you're looking for a good way to "jump start some growth", my opinion is that you should do a strength cycle to bring up your poundages. This fits in perfectly if you're towards the end of your HST cycle. You'd probably see better strength gains using lower reps than GVT has you using, though. You might consider something like 5x5 or 3x3, or even just doing a few extra weeks with your 5 RMs. Just be sure to stay away from failure.