I definitely would. After all, everyone will come out happier; both parties will get a relationship they're looking for. As long as I'm 100% sure the girl likes me, can enjoy being around her, and know she won't lose interest quickly, it'll be a happy relationship for me. I don't see it as "taking advantage of her". Regardless of whether or not I was physically attracted to my girlfriends in the past, I always treated her very well and made sure she had the best relationship I could give her. In the end, by starting a relationship me, the girl has nothing to lose, and a lot to gain. How so? She'll get a boyfriend that's faithful, treats her well, and makes her feel special. In the end, I see nothing wrong with dating someone just to be in a relationship, as long as you make the relationship feel good.
Look at it this way. A guy can generally date a girl he's not attracted to if he sees the benefit in that, but a girl will never date a guy she's not attracted to. So what makes a difference is not how much he likes her, but how much she likes him.