When you finish "lingua latina per se illustrata" can you understand latin books easily?

I've heard it said that it takes about 10 years of study to gain a real facility at reading Latin. My own experience bears this out.

That said, with a good dictionary and a lot of hard work, you ought to be able to struggle through a typical Latin text after studying a year.

I think Oerberg's course is as good an introductory course as any. It can be completed in about one year. After you've completed it and you are working with Latin texts on your own, you might find you want a more systematic grammar for handy reference, as a complement to your dictionary. Such references can be found as free PDF files on the internet.

But, if you literally mean a medieval manuscript, then the answer is no. I've been reading printed Latin text for years, and I still cannot read a manuscript. I can barely make out the handwriting at all, and most manuscripts I've seen make copious use of abbreviations, few of which you will learn from reading Oerberg, or any other first year textbook.