I think that's most likely an urban myth for JWs to try and bolster their belief that they are close to the end and that it's imminent. What better way that the org making plans like that ...
If they actually, really genuinely, believed that the great tribulation was coming - they would be doing something concrete like storing caches of survival rations. The idea that the end of the world would come and they would carry on printing leaflets and distributing them is kind of laughable and ignores simple logistics:
The power is still on
The internet still works
They are still free to drive around and deliver to congregations
Publishers are still free to go door-to-door and hand out their propaganda
Everyone can still get gas then ...
... where's the persecution, the great tribulation? Sounds more like every-day routine!