Re: JS1000 w Heavy Gauge (13.) strings?
The truss rod will probably want a bit of an adjustment to keep the action nice along the length of the neck, but there's nothing inherently dangerous about using heavy strings. The strings themselves will fail from high tension long before the neck will.
The bridge could be a problem, depending on what you'd like to do with it. You probably could still get it set up to float even with the heavy strings, but you'll be adding at least one more spring to the back and possibly need to look into stiffer springs too, all of which will, of course, lead to a much firmer feeling trem, which many people don't care for. If you don't care about the trem, just look into blocking it, there's no reason to replace it.