I was up in the area on saturday. It was very active with the storms. Admittedly I did not climb Humphreys. However, I did climb Sitgreaves nearby. If the weather is active, you still have a reasonable chance if you get a very early start and can be at the top by 7 or 8 a.m., meaning a pre-dawn start. The thunderheads were starting to build by 9 a.m. or so. It's a calculated gamble.
I think the monsoon has been very busy this past week, moreso than usual. I did see the break in the pattern at least for the southern deserts on the various weather sites, so I echo Lionel above. However, even in normal monsoon conditions, you want to be down and back in the trees by mid-morning.