I'll take a shot at it. I'm not a doctor, but it would seem plausible to me that it could affect performance the closer you get to the point of being out of breath (the Ventilatory Threshold). This website seems to have a lot of people on it asking very similar questions.
www.thalassemiapatientsandfriends.com
I googled "Thalassemia Minor endurance sports" and that website came up with several forum topics. I'm always hesitant to take everything said on forums with full value, but it does seem many discuss common symptoms of having Thalassemia Minor (Longer Recovery Time between exercise, slower than anticipated during exercise, etc.). Anecdotally, it appears there were several people on that forum that completed marathons but felt as if their performance was hindered by the condition.
I wasn't able to find many scientific articles on the condition and endurance sports measured directly. One of the articles I could find (linked here) gave a brief overview of Thalassemia Minor and in addition the effects of low Hb and possible treatment.
The most interesting thing I found during this research adventure was that tennis legend Pete Sampras and soccer legend Zinedine Zidane had this condition and excelled at their area of sport. I believe that their level of achievement in their sport would show that competing in running events and Thalassemia Minor can coexist. I would definitely talk to your doctor about it though as they can give you professional advice as long as they are well informed about the condition itself. It seemed like hydration, deep breathing, and change in nutrition were common suggestions from other people's interaction with doctors.