Yes, if you have a Home or Professional subscription. Both endpoints (that is, the remote computer you want to control, and the device you’re sitting in front of and want to control from) must be connected to the Internet, and able to communicate with RealVNC services.
If you have an Enterprise subscription, the answer is also yes if you wish to establish cloud connections to a particular computer.
If you have an Enterprise subscription and wish to establish direct connections, then endpoints need only be Internet-connected if you’re actually routing the connection over the public Internet. If you’re routing over a private TCP network such as a LAN or VPN, there’s no such requirement. Neither VNC Server nor VNC Viewer ‘phone home’ in this circumstance.