Yes. Either can probe any reachable IP address, whether that be a public address on the Internet or a remote private LAN address via VPN tunnel. Nagios, being open source, has no restrictions at all. PacketTrap licenses its products by the number of nodes monitored, with 50 being the lowest number. Those nodes, however, can have any IP address anywhere reachable from the PacketTrap machine. You might also check out Intermapper (Intermapper.com) and PRTG (Paessler.com), both of which have free versions limited to a small number of devices. I find these much easier to use than either Nagios, which I used for years but gave up on, or PacketTrap, which I tried but has much too limited for what they charge. Intermapper and PRTG compliment each other, even though the do somewhat compete.
