Oh, it does...at least, the processor reports in Windows as "64-bit capable" and contains the "lm" "long mode" flag in Ubuntu.
But my Ubuntu installation, like my Windows installation, is 32-bit. Poking around, I pretty much need to do a clean install of 64-bit. Yuck. I'll obviously try the live CD first to make sure it runs.
While I looked, I found that Ubuntu still seems to be recommending the 32-bit version (https://help.ubuntu.com/community/Installation/SystemRequirements), so this problem is probably pretty common. If Opera already supports 64-bit, wouldn't a 32-bit build be as easy as changing some compiler options? This seems like a pretty easy fix to make it MUCH more accessible.