This is, of course, a matter of opinion, but I would argue that they can. This is a long-standing argument over whether "descriptive representation" is necessary.
Some argue that a person who is not like their constituents in important ways (class, race, etc) cannot represent those consituents. However, I would argue that any person can understand the concerns of other people and can represent those concerns effectively.
Look at this in terms of everyday life. Can parents effectively "represent" children or do they not understand them? I would argue that parents can listen to their children and understand their needs. They can then act to fulfill those needs.
In just this same way, a person who is different than I am can represent me. They do not have to share my background in order to be able to understand my needs. All they need is to be willing and able to listen with an open mind to what I say.