The data won't be copied, but kernel has to reserve the memory for both processes.
If kernel could not reserve memory for forked process, overcommit would not be necessary.
Only without overcommit does the kernel does need to start accounting for hypothetically-writable memory before it actually is written to.
What overcommit enables is more efficient use of memory for applications that request more memory than they use (which is most of them) and more efficient use of page cache. It also pretty much guarantees an app gets memory when it asks for it, at the cost of getting oom-killed later if the system as a whole runs out.