Your client machines have only VPN connectivity, and it is not possible to resolve the machine hostname into an IP address. You want to know whether it is possible to scan client machines in such an environment and for the Agent to initiate a scan and send the results to the GFI LanGuard server IP.
LanGuard requires the hostname to resolve into the actual IP address (and IP address into the hostname) to function properly - Forward and Reverse DNS Lookup is one of the base Network Connectivity prerequisites for the successful LanGuard operations.
Ensure that machine names and IP addresses resolve correctly. Seek the help of your system and network administrators, since this heavily depends on your environment and VPN solution. For example, adding the LanGuard server name and IP address to the hosts file on the client machines is a valid shortcut covering the requirement from the Agent side, but wouldn't help the LanGuard server name/IP resolution of client machines, this should be solved on the VPN+AD side.
Without proper bind between the Hostnames and IP addresses both for LanGuard server and client machines, LanGuard would not be able to scan and remediate the client machines, and the Agents wouldn't be able to communicate with the LanGuard and send back the results. This includes the scanning failures in situations where a machine has two IP addresses bound with a single FQDN, for example, a machine that has two separate IP addresses when connected to the organization's network directly (on-premise) and through a VPN connection.