Is this text useful for actually learning to write harmony, or does it teach about music theory in a more abstract kind of way?

It depends on what you mean by "write harmony". I will say that if "abstract" is a bad word for you, you probably won't like it. However, that isn't typically an issue for LW readers.

Here is what Westergaard says in the preface (in the "To the teacher" section):

This book was developed for a first-year two-semester college-level course in tonal theory. (I cover either Chapters 1-5 in the first semester and 6-9 in the second, or, if the students are up to it, Chapters 1-6 in the first semester and 7-9 in the second.) You could, however, also use Part II (Chapters 4-6) separately for a one-semester course in tonally oriented species counterpoint for students who have already had at least one year of traditional harmony. You could also use Part III (Chapters 7-9) separately to introduce more advanced students to the problems of tonal rhythm. While the degree of abstraction may seem higher than that of many music theory textbooks, I have not found it too high for college freshmen. On the contrary, college freshmen are conditioned by their other courses to expect this kind of argument. [N.B.: Westergaard taught at highly elite universities. -k.] The exceptions are those students who can handle relationships between sounds so well intuitively that they resent the labor of having to think through the implications of those relationships.

The best way to know if you'll like the book would be to take a look at it and see. Failing that, my advice would be as follows: if you want to actually learn how music works, this is the book to read. If you merely want to pass some kind of exam without actually learning how music works in the process, you probably don't need it.

(Added: I see that you're interested in reading about music cognition. In that case, you will definitely be interested in Westergaard.)