They would still be in the same area, but new ones wouldn't have grown yet to replace the ones that have been harvested thus far. This means that resources on these mushrooms could start to become scarce through this month. Sourcing new ones, and in a much larger abundance, will become an option in the very near future like the event, but at this current time, they can only rely on the known location.

I too suck at giving exact distances, but I'd say that yeah, that would be possible, so long as a Sleeper was the one carrying the mushrooms and not the dragon.