I'm running at full duplex.
Theoretically, the modem should offer enough protection that a surge would damage the modem and nothing else. The Ethernet should be isolated, assuming it conforms to standards. Since the modem is plugged into a surge protector, I should have another layer of protection, but a surge protector isn't as much protection as a UPS offers. For 100% safety, I'd probably want the modem on the UPS. Even if I'm essentially 100% protected now, it wouldn't be a horrible thing to have my modem available if I lost power, assuming the network itself didn't go down with the power outage.