Cold Steel: " What would the reaction of the church be if one of the Governing Body claimed to have seen an angel or have an angelic experience?
By "angelic experience" I mean being shown future events by an angelic presence. "
It would be a disaster for the WTS of one of the gb claimed a direct communication with a supernatural entity of any kind and it was made public.
The reason is that over the length of its history (about 140 years or so), the WT has made a lot of outright predictions and a few guarded predictions about the end of times, Jesus's second coming, armageddon, etc. All have failed to materialize.
The gb wiggles out of these failures by claiming they (the gb) are only "spirit-directed," not in actual communication with angels or god or whatever. They don't claim to be direct prophets of God. This allows them to rewrite their history of failures and keep their adherents in line by claiming that God's "light" (that is, his indirect guidance) keeps getting brighter as "the end" approaches.
There are no magical gold tablets or peep stones" or directly "revealed" info about "future events" in the dub religion.
That's sort of thing is the province of Mormons.