Well, we do research on nearly any topic you can think of in the orbit of music's technical elements, history, interaction with culture, and interaction with individual people. There is a slowly-eroding bias toward working on "classical" music, i.e. music of the Western European "art music" tradition, although musics from outside that tradition are (as of the last couple of decades) now entirely accepted as legitimate at least in principle, and have attracted quite a bit of scholarship since they were under-studied until recently.

A few examples of the kinds of things music scholars might do:

• Examine documents in an archive in order to elucidate some episode in music history (pretty much exactly what many "regular" historians do)
• Use primary-source research (often conducted by others) to spin a broader narrative about the trajectory of music history in some time or place -- often bringing together historical, cultural, and technical elements
• Visit some unfamiliar music-culture and document its social and technical elements -- in the old days, this always meant some far-flung part of the globe, increasingly these days is done anywhere a distinctive social practice around some kind of music exists (this approach in all its incarnations is known as "ethnomusicology")
• Construct a controlled experiment to test some aspect of what is going on in people's brains when they hear, perform, or otherwise participate in music
• Examine anywhere from one to thousands of musical compositions in order to describe or analyze their features or structure. When one or a few pieces are involved, this will tend to focus on what is distinctive about the composition(s); when many are involved, it will tend to generalize about broad tendencies and similarities. The actual method of analysis varies extremely widely depending on the repertoire and the analyst's interests and orientations.

The field has largely moved on from its 1990s-era infatuation with postmodernism and a reasonably high level of scholarly rigor is present -- this is not to say that no junk gets published or that music scholarship ever does (or should) resemble an exact science.

A few things that distinguish the best professional music scholarship from crankery:

• While pretty much all professional music scholars do really like at least some music, we tend to be aesthetic relativists at least enough to avoid this kind of trainwreck (it's a website whose author suggests some metrics by which we might determine that some chord progressions, melodies, etc., simply are better than others). Music scholarship has enough robust results to be quite sure that nothing like that could possibly be the case. Like most modern linguistics scholars, our basic orientation is descriptive rather than prescriptive, which is strikingly infrequently the case among cranks. (Of course, since music is nearly always in part an aesthetic object, music scholars can and do express aesthetic judgments, we just know better than to confuse them with any "absolute" notion of correctness.)
• We're very comfortable with the fact that music is a cultural product, and not metaphysically special in any way -- although it is a very, very complex phenomenon and frequently harder to discuss in very concrete terms than some other kinds of cultural products seem to be.
• We rely on painstakingly gathered data wherever possible.
• We maintain a professional expectation that we know not only the history of music but the history of our discipline, which helps us avoid rehashing the same problems others were struggling with in past centuries. Cranks often reinvent various square wheels that were long ago either dispensed with or refined into usable ideas.
• We have good peer review and few enough journals that most published work has been vetted for glaring problems and does meet certain minimum standards.

I don't claim that these standards are met in every published piece of music scholarship, but they are what the profession aspires to and usually attains. I don't think music scholarship is as difficult as science assuming the necessary preparation, but the fact is that the necessary preparation in terms of gaining fluency with music notation, music theory, and music history takes a long time and is a high bar to clear for most people who aren't professionals.

Do you think that a person can truly appreciate something without fully understanding it?

Short answer: yes.

Longer answer: I don't believe in "true" appreciation of aesthetic or cultural artifacts as being distinct either practically or metaphysically from whatever other kinds of appreciation or quasi-appreciation there are.

Long answer: I certainly do consider some basic literacy in music theory or music history to be part of a good education, just because it is a major cultural product that nearly everyone consumes a lot of. In the course of receiving that education, some people will find that it enhances their enjoyment of music. (Some don't, though! And they always make sure to tell me about it! Including on my course evaluations!) People who are in favor of that kind of knowledge-enhanced enjoyment tend to elevate it with the prestige term "appreciation." The thing is, though, that people's aesthetic experiences and reasons for liking music and personal uses of music vary a lot. Since liking music in whatever way and for whatever reason really doesn't involve holding factual beliefs, I'm at a loss to see what good I'd be doing by going up to some guy who likes music and telling him that he's right to like it but that he likes it for the wrong reasons.

About as far as I'd go is to say that, since pleasure is good, most people should consider learning more about music to see if it enhances their pleasure in it. If it does, great. If it doesn't, they should stop. It's not a one-size-fits-all situation.