From http://nwavguy.blogspot.ro/2011/07/o2-headphone-amp.html graphs looks like output power for 16 ohms and 32 ohms headphones doesn't being affected at all when running from batteries and we're speaking about a massive voltage drop from 12V regulated to 8.4V batteries. So, if your power adapter is having 13.5V output, then feel free to test the voltage when powered on with music and headphones connected (just be sure you know what you're doing, 'cause a small short-circuit will make your O2 defective), but I really think it will be at least 12V.
If there's anything from your output voltage to loose by using this power adapter, then it's at most 0.5V on your headphones plug (instead of 7.3-7.5V you'll probably get around 7V), but hey...your opamps will be a bit cooler this way, same for mosfets. :)
In your place I would stick with this power adapter, but if you really believe this will impact the performance of your O2 in the future, maybe it would be better for you to return it and exchange it for a bit more expensive 14-16V power adapter.