For the record, I did buy a straight-through 'extension cable'. After connecting the serial cable and installing the Cyberpower PowerPanel Personal Edition software on my normal Windows 8 desktop, I shut it down and moved the PC to one of battery-backed outlets on the UPS. Booted back up and on first opening it up things looked promising - the Cyberpower monitoring utility was showing the status as running on electric power and the battery charging.
It has been plugged in over 10 hours now so it should be fully charged, but to at least show this looked like the serial connection between the two was working properly. I tried simulating a power outage with my main desktop PC hooked up (tower only) and while my main desktop is probably over the load rating for the UPS it didn't run even a second -- just cut right off when I pulled the plug, no alarm or anything from the UPS. The only thing I'm sure of so far is that the battery is dead. Brocade Silkworm 3900 Firmware Download here. I also had trouble getting the unit to power back on once I plugged it back in. Seemed to be internally cycling.
But got that resolved. Anyway, I thought I'd do a second test, this time with something not-really running on it. A shut down laptop connected to the battery backup and the PC fully powered elsewhere. The idea was I could still read the Cyberpower monitoring software on the PC when a 'power outage' occurred. When I unplugged the UPS's mains line, the AC adapter's plug light on my iBook went out immediately -- signalling it was not getting any power from the Cyberpower's battery (and it's certainly within the load rating for the unit -- even when running).