Hopefully, your answer to the question in the title of this post is an unhesitant: "Yes, of course, I would. A wheelchair makes no difference to me. What matters to me is who is sitting in it."
Unfortunately, in my experience, most people don't seem to feel that way, unless they themselves are confined to a wheelchair. Honestly: would you openly date and marry a person confined to wheelchair? The question here is directed at non-wheelchair users (which include myself).
Some of you may reply "yes," because it is in line with your ideology, because it would be politically incorrect to say "no," or because you are happily married, and there is no conceivable chance (in your mind) that you will ever date again.
But would you? If you were single and went to a party that was "happening," and you spotted an attractive girl in a wheelchair (or guy in a wheelchair), would you consider chatting her up? Or would the very thought of hitting on her make you feel embarrassed, not least if you were in the presence of your friends?

The most realistic answer to these questions is that even if the hottest girl at the party were the girl in the wheel chair, you would check out the second-hottest girl.
Social stigma can be a significant deterrent. But people have walked on fire to get a girl (or guy) they were attracted to. History has too many examples of this to pick one that is adequate.
Why is a wheelchair a hindrance? Is it because you are only focused on what your relationship looks like to other people? Is it because you think wheelchair users cannot have sex?
If it's the latter, you are wrong. Wheelchair users have sex. Even if they cannot move their lower body, they can have erect penises and sensitive clitorises. Different muscles and nerve endings are affected by different types of accidents.
But maybe your worry is not the sex but what your friends and family would think and say. They should not be concerned about your love life, but if they are, here is a good comeback if you do decide to go against the norm:

If I had been in an accident and were in a wheelchair, I suppose you would find it inappropriate for me to find love? You would scare off potential (abled) suitors, yelling: "For God's sake, don't go near her. Her lower body is paralyzed. She is in a wheelchair." I hope not!

If you are a caring parent, you would never think that way about your own child. You would feel that any abled or disabled partner would be lucky to date her. But now the roles are reversed. Your little kid (who is now approaching adulthood) is not disabled, yet (let's imagine) she is dating a disabled guy in a wheelchair.

You may be one of those politically correct parents who is not expressing any concerns about your child's new relationship openly. But if you are like most people, there is a part of you that doesn't like it. "My kid is not disabled. Why should she have to date a disabled guy in a wheelchair?"
The good news is that we can overcome these types of implicit or not so implicit biases by standing up to the stigmas we are surrounded by. Our family and friends are not our romantic partners. They may once in a while have good advice on love and relationships. But they are narrow-minded. A person in a wheelchair deviates significantly from what our family envisaged for their pristine (abled) daughter (or son). They forget that no relationship is smooth sailing as the years go by. Relationships are hard work. In the long run, it doesn't matter what your physical appearance is like. What matters are your personality and character.
Berit "Brit" Brogaard is an author of The Superhuman Mind and the author of On Romantic Love.