Depends on what the part is. If it's a part they would never stock (vintage bars, or your dear departed grandad's favorite old Brooks saddle), then clearly you could provide it. At the other extreme, it's a common part that they have (say, inner tubes or cables), it would be kind of tacky of you to expect to be able to bring them to save a few slim bucks. It between those extremes, you may need to negotiate. It may depend on how much gall you have, in some cases