Gym reset?

I believe they did not state they will be disabling gyms during the start of the event. Nevertheless, the last time Niantic made some changes specially the Pokémon's CP, they did return them to us perfectly alive and healthy. Probably they will do the same when they disable the gyms.

Nah the gym reset will be after the event is over.

"Soon thereafter, you can look forward to a new update focused on collaborative group gameplay features that will get you playing Pokémon GO in fun new ways. In preparation for these exciting features, we’ll be temporarily disabling Gyms for a short period of time."
https://pokemongo.gamepress.gg/news/celebrating-first-anniversary-pokemon-go

Why should we know that? lol
There is nothing in the Patch notes / Event notes.
You will see ;)

According to the PoGo Italian offical anniversay announcement the gyms are going to be disabled on June 16th. Of course they removed the date soon after because none of the other languages sites showed that date, but it was too late to try to hide it. So we can almost assume that that will be the day.

About when they will come back still nothing leaked, my guess is that July 22th could be day, just when the Chicago event takes place so people can enjoy the new system during that event, maybe a bit earlier who knows.