Correct while the Stratos has XLR inputs, it isn't a balanced amp per se. The two inputs - XLR and RCAs internally are wired together. While the Stratos isn't a balanced amp, I don't believe that you will notice any system degradation by utilizing the Stratos XLR inputs.
I am definitely NO expert on the subject but from what I have read on various audio forums, the "supposed" benefits of balanced inputs are of questionable value anyway. I believe there are noticable benefits when using ICs of considerable length but it is typically best to keep ICs short anyway. Also I believe there are no standards on how the balanced inputs are wired so it can be problematic to get stuff wired together correctly. Did I already mention that I am not an expert on this subject

Therefore, I would recommend that you research this topic if you clarification on this subject.
Hope this helps
There are a post or two on the Odyssey AC forum where Klaus himself weighs in on the balanced amp question. A quick search on audiocircle / Odyssey forum should help answer your questions.