VoIP will be unable to function without an internet connection. VoIP phone calls are made via the Internet, rather than over traditional phone lines, and are free. This implies that if the internet connection is lost or breaks down, the capacity to make phone calls is also lost or compromised.
However, with the additional features provided by some Hosted PBX services through VoIP, or in most situations even with fundamental SIP trunking service, you can implement a disaster recovery plan that would allow all phone calls to be forwarded to an alternate number, such as a cell phone or an alternate office location. This would be useful in the event of a power outage as well as the loss of an internet connection.
It can be configured as an automated failover, and you may or may not be required to do so in advance, but the hosted PBX provides you with the opportunity to go into a web portal and make changes on your own, rather than having to wait for someone else to do so for you. This can be accomplished with a smartphone internet connection or a personal computer.