No, "у меня" is always related to "me". Literal translation is "by me" but it can have different translations to English depending on the context: "in my..." ("у меня в..."), "at my place." ("у меня."), and sometimes even "I have" ("у меня красивое имя" - ("I have a nice name").
I only spoke Russian as a child so native speakers feel free to correct me or provide a more accurate explanation.
Oh maybe you meant that "у меня" can refers to the luggage therefore it can be translated to "my luggage" as you said? In this case, my answer is still no but the explanation is different: "у мена в..." means "in my...".
If I wanted to say "My luggage is in the room" I would say "Мой багаж в комнате" or "У мена багаж в комнате" which puts more emphasize on this fact being true about me. Like if my parents are mad of my brother for leaving his luggage at the living room and I want to annoy him, I would prefer "У мена багаж в комнате" over "Мой багаж в комнате" which only emphasizes the word "room".
Well maybe you can say "Багаж у меня в комнате" like "Багаж у меня - в комнате" but being written without a dash and with no context of me listing where I tend to put stuff, this is most definitely not the first translation that comes to mind.
Again, I'm not exactly a native speaker so please correct me if I'm wrong.
"У + genitive" can carry the meaning of something mentioned or unmentioned that belongs to you. It is often a part of your body, your house, or your belongings.
For example: "Отец у сына." means "The father is at the son's."
So, "У меня в комнате" means "At mine, in the room."
Here меня probably refers to a house or something.
But "У меня в ухе" is literally "At mine, in the ear."
Clearly, at my house in the ear doesn't make sense, меня refers to your body.
The thing that's making this difficult to grasp is the presence of the preposition B. At first glance, the sentence comes across to me as "my baggage is in the room" rather than "the baggage is in my room" - because, literally speaking "багаж у меня" appears to mean "The baggage by me" = "my baggage", followed by "в комнате" = "in the room".
Is this obviously wrong? If so, I'd really appreciate knowing why it is, and how the presence of the preposition operations. If "у меня" is used instead of some form of мой, then "мой в комнате" seems awkward.
Unless, of course, the entire phrase "у меня в...." has an idiomatic translation in to English.