The question seems to be about two different things. The title question says, "Is partimento a good way to learn how to write a trio sonata in the style of Corelli?" Sure, if you want to learn how to imitate the specific style of that particular period, using historical pedagogical methods is probably the best approach, though you'd likely need a good teacher. Partimento is only part of the types of training Italian musicians would have received at the time of Corelli (you'd also need to learn other patterns of imitation, melodic construction, traditional singing instruction which would have been very much a part of pedagogy, etc., etc.), but it's definitely closer than most modern pedagogical methods. That's how young musicians learned stuff like that back then. For an example of a modern young person raised in that method, search for Alma Deutscher. Note that this method is traditionally very "hards on" and again requires a knowledgeable teacher who can improvise effectively in styles from around 1700. There are very few people like this in the world.
But the rest of the question goes off of the premise that such study "will provide a good framework for my understanding of counterpoint and harmony for classical music in general." I suppose that's likely true of classical music in the period of maybe 1675-1800, particularly Italianate styles. (If you want to understand North German music from this period or French music, you'll need to look at related historical methods from such countries.)
But it's certainly not an "efficient and pragmatic" method, especially if the goal is to learn to communicate with other musicians about the way they think classical music works.
I certainly believe that partimento is more likely to give you a sense of how the music of that time (again, particularly in most Italian styles) was constructed than most modern music theory. But it's something that would have been studied historically with a teacher over many years.
Modern music theory textbooks have created shortcuts of a sort intended to try to present a sort of grammar of classical harmony in 2-4 college semesters. We can argue about how efficient or effective it is, but it's certainly shorter and the de facto way most musicians talk about music theory.