Besides this boycott is at best useless, most are only going offline for 48 hours; it should be permanent until they reverse the decision if they were being sincere.
The third-party apps shutting down on July 1st will be the real test. If Reddit notices a significant drop in traffic on that day, they will probably start walking back the change. I agree that this boycott, while the intention is good, won't do much.
Unless a large number of people who don't use 3rd party apps also leave in solidarity, it won't be a "significant drop". 3rd party apps make up quite a small amount of total traffic. And that's also assuming that TPA users _leave_ and don't just switch.
If you have 10,000 users you have 1000 commenters, 100 people posting, and 10 moderators. If you keep 97% of your users but you lost half your mods, 25% of your posters and 7% of your commenters its going to lead to an eventual decline bigger than 3% and it can create a self re-enforcing trend because the people contributing to other networks can drag their connections along with them.
I don't think Reddit is doing anything based on that day's data. I suspect that they will wait for a month before starting to rely on the data for any long-term prospects.