MGB: You PM'd me, but I wasn't able to reply. Turn your PMs on!
There are many that can answer this, but here goes. Hood gets climbed in late August all the time. BUT, it's an ugly and relatively unsafe climb. Lots of rockfall, and potentially bomber steep ice through the Chute (Pearly Gates--but they are anything but that in August--loose rock is more like it.).
Definitely a hardman thing to do combining it with the H2C relay. So, if you go, bring a helmet, climb fast, and be VERY aware of what's happening above you. May need a second tool for the crux in the Chute. Depends on your comfort level. I've climbed it year round, and this is approaching about the worst time you could do it. That said, good luck. Have fun!