It says state. Copy on write still means it's O(number of page table entries) even if you don't copy the contents. It's a well known issue that forking a program with large virtual memory size is slow.
On modern hardware a cow page copy should only take 1-5ms. Redis forks to save the db to disk and it's been a solid design choice.
I guess it depends on how sensitive your application is to main thread pauses.
It says "(including memory)". It's pretty natural to read this as "(including the contents of allocated pages)".