I repeatedly used gore-tex trail runners (Asics, very comparable to the New Balance) trail running in Massachusetts August and September – at the end of a 1 or 2 hour run, my feet were hot and sweaty. Not horribly so – I wasn't uncomfortable – and really only noticed at the end when I stopped. Never got any hot spots. But I think it is safe to say that hiking all day on a hot dusty trail, your feet would also be hot and sweaty. I don't think I'd blister, though it wouldn't be my first choice of shoe.
(I used them because I wanted to see how breathable they were – the answer: not very. But they were tolerable. And they were great on fall hikes. I think I used them for one summer overnight here in MA – with wool socks – and while my feet were sweaty it wasn't a huge deal. Keep in mind that I don't sweat a lot/overheat very much.)
If your son is going in a few weeks – I'm assuming it is going to be snowy and cold. How cold, I have no idea. When temperatures drop to around zero, trail runners no longer work for me. But that being said, hiking with the WP trail runners I have gotten down to as low as 5-0 degrees and have been ok as long as I kept moving. I haven't used my non WP trail runners hiking – only for winter running. Just because while they are great with breathability and even wicking moisture – I know the odds are pretty high I'll encounter wetness on hikes/snowshoeing and would prefer the extra insurance that even not quite 100% WP shoes brings me, in temps that cold when I'm out for more than an hour or two. (the goretex trail runners failed in wet conditions – no rain, just wet trail, at around 200 miles. But they have done ok in wet snow, although crossing a few semi-frozen streams I can tell some water has gotten in. Not enough to be an issue though.)
He could buy the WP ones, use them for this trip, and then hold onto them for hiking in cooler temps – I know you are located in California so it's not that cold but on days that are wet and cold they would be usable. Then you'll still be getting more use out of them than just one trip. And your son can stick to what he likes in hot weather. That's pretty much what I do. I do prefer the non WP in any temp above freezing though.