Yes, it matters at the beginning of a loving relationship. If you are good looking, then you'll get more chances. Everybody loves good looking guys/women. We all know about love at first sight. If you are very ugly, how can that happen? Unless you are special, others can feel that at first sight. A good looking person is usually very confident in their looks, which is good for a loving relationship. Let's say there are a smart, nice and good looking girl friend and a smart, nice and ugly girl friend, which one would you choose? (这句里的"there are a smart..."不要误会了,“are a”在这里没有语法错误,因为我讲的是两个人.)
But the thing is, "a good looking person" doesn't mean everything in a loving relationship. Your personality is more important. Some people are not good looking, but they are confident, smart, open-minded, humorous, understanding, optimistic, well educated, etc. Those confident people make themselves look good.
One of my friends, Sara, is a very good looking woman. My other friends get shocked by her unbelievably pretty face. Her husband married her because of her appearance. After they got married, they had many problems. She is dependent, has no money and couldn't take care of her little daughter. She didn't want to fix the problems and chose to complain about everything. I tried to help her but I failed.
So looks do matter in a loving relationship, but only a little, at the beginning of a loving relationship.
PS：题目Looks do matter in a love relationship中的love最好改成loving,更妥当一些.