On recent kernels where SO_REUSEPORT is finally implemented (3.9+), this dead period does not exist anymore. While a patch has been available for older kernels for something like 10 years, it's obvious that many users cannot patch their kernels. If your system is more recent, then the new process will succeed its attempt to bind() before asking the previous one to release the port, then there's a period where both processes are bound to the port instead of no process.
There is still a very tiny possibility that a connection arrived in the leaving process' queue at the moment it closes it. There is no reliable way to stop this from happening though.