If you're on a domain-joined computer with functioning Certification Authority, yes, this is what should happen. This is covered in the documentation at
https://www.yubico.com/support/documentation/ under the section "Using YubiKey PIV for Smart Card Login" (the five documents are intended to be followed in order, skipping any of #3 - #5 depending on what implementation method is used).
This certainly isn't intended for a standalone home-user environment.
Proper implementation in a domain environment would allow you to plug in the YubiKey 4 / NEO and either log in to your user account with it, or use it to remote connect to another domain-joined computer.