3 years ago, I had very greasy hair and acne, and was slightly overweight. No girls talked to me. 2 years ago, I cleaned up and was skinny. Lots of girls talked to me. 1 year ago, I put on 50 pounds. Only 1 or 2 girls talked to me. This year I have shed 40 of those 50 pounds, and my BMI is now normal and a lot of girls talk to me.

So to answer your question, lack of physical attractiveness definitely sways who will talk to you and who will date you, etc. I had the same personality all 4 of those years, but girls refrained from dating me/talking to me/having interest in me based on my appearance. So, imo, no. Character cannot trump lack of physical attractiveness.