Not the GCT, but we camped just north of Tuolumne Peak this weekend, not far from the Canyon as the crow flies. We were looking at Falls Ridge and upper parts of the canyon from our campsite. Skeeters were bad from about 9000' to at least 10000'. Last weekend it was worse in the Lyell Headwall area from 9500-10,500', so I'm thinking skeeters won't be a problem in the canyon itself... but the flies were already starting.. and in the canyon, I'd expect them - I gently suggest you bring a headnet.
Big concern for me would be the heat at least through Thursday. As mentioned in a previous post, stay hydrated. Don't overheat. Pate Valley will be HOT. And in the past, I found it humid and hot, which drains me.
Saturday
night at 10,000' the lowest temp any of us saw was 60 degrees just before dawn. At 4000' in Pate Valley... ugh.. if anyone went, hopefully they'll respond..