Hi!
Actually, that is way better and much faster (in terms of search) approach in my opinion, as returning the product, based on the PDF content is not possible (because those are two separate post type objects, not one). PDF content indexing would only be able to return the PDF files (or parent pages attached to it) as results.
The plugin will index the additional search tags field, and it should work as you expect it. I can recommend this solution.