Yes, if by "connected to a VPN" you mean two things:
1. You are connected to a trusted network via a VPN protocol. A trusted network might be your home network, a network you operate at a data center, or a network you operate at a cloud provider such as AWS or Azure.
2. You are not using split-tunneling, which is surprisingly common with some VPN clients. Split-tunneling will only send traffic destined for the remote network's address space to the VPN endpoint, sending all other traffic to the local network's gateway (in this case, the rogue router). You will want to disable split-tunneling in order to send all traffic to the VPN endpoint.
It has become popular to refer to connecting to a third-party proxy service that uses VPN protocols as "connecting to a VPN," but if you do that, you are putting your trust in a third-party vendor of proxy services. IMO it's superior to just operate your own private network using a more trustworthy data center or cloud provider.
1. You are connected to a trusted network via a VPN protocol. A trusted network might be your home network, a network you operate at a data center, or a network you operate at a cloud provider such as AWS or Azure.
2. You are not using split-tunneling, which is surprisingly common with some VPN clients. Split-tunneling will only send traffic destined for the remote network's address space to the VPN endpoint, sending all other traffic to the local network's gateway (in this case, the rogue router). You will want to disable split-tunneling in order to send all traffic to the VPN endpoint.
It has become popular to refer to connecting to a third-party proxy service that uses VPN protocols as "connecting to a VPN," but if you do that, you are putting your trust in a third-party vendor of proxy services. IMO it's superior to just operate your own private network using a more trustworthy data center or cloud provider.